PINTO, Andressa S.; CHEDID, Marcio F.; GUERRA, Léa T.; ÁLVARES-DA-SILVA, Mario R.; ARAÚJO, Alexandre de; GUIMARÃES, Luciano S.; LEIPNITZ, Ian; CHEDID, Aljamir D.; KRUEL, Cleber R. P.; GREZZANA-FILHO, Tomaz J. M.; KRUEL, Cleber D. P.
2016-01-01
ABSTRACT Background: Reliable measurement of basal energy expenditure (BEE) in liver transplant (LT) recipients is necessary for adapting energy requirements, improving nutritional status and preventing weight gain. Indirect calorimetry (IC) is the gold standard for measuring BEE. However, BEE may be estimated through alternative methods, including electrical bioimpedance (BI), Harris-Benedict Equation (HBE), and Mifflin-St. Jeor Equation (MSJ) that carry easier applicability and lower cost....
Pinto, Andressa S; Chedid, Marcio F; Guerra, Léa T; Álvares-DA-Silva, Mario R; Araújo, Alexandre de; Guimarães, Luciano S; Leipnitz, Ian; Chedid, Aljamir D; Kruel, Cleber R P; Grezzana-Filho, Tomaz J M; Kruel, Cleber D P
2016-01-01
Reliable measurement of basal energy expenditure (BEE) in liver transplant (LT) recipients is necessary for adapting energy requirements, improving nutritional status and preventing weight gain. Indirect calorimetry (IC) is the gold standard for measuring BEE. However, BEE may be estimated through alternative methods, including electrical bioimpedance (BI), Harris-Benedict Equation (HBE), and Mifflin-St. Jeor Equation (MSJ) that carry easier applicability and lower cost. To determine which of the three alternative methods for BEE estimation (HBE, BI and MSJ) would provide most reliable BEE estimation in LT recipients. Prospective cross-sectional study including dyslipidemic LT recipients in follow-up at a 735-bed tertiary referral university hospital. Comparisons of BEE measured through IC to BEE estimated through each of the three alternative methods (HBE, BI and MSJ) were performed using Bland-Altman method and Wilcoxon Rank Sum test. Forty-five patients were included, aged 58±10 years. BEE measured using IC was 1664±319 kcal for males, and 1409±221 kcal for females. Average difference between BEE measured by IC (1534±300 kcal) and BI (1584±377 kcal) was +50 kcal (p=0.0384). Average difference between the BEE measured using IC (1534±300 kcal) and MSJ (1479.6±375 kcal) was -55 kcal (p=0.16). Average difference between BEE values measured by IC (1534±300 kcal) and HBE (1521±283 kcal) was -13 kcal (p=0.326). Difference between BEE estimated through IC and HBE was less than 100 kcal for 39 of all 43patients. Among the three alternative methods, HBE was the most reliable for estimating BEE in LT recipients. Estimativa confiável do metabolismo basal em pacientes transplantados de fígado é necessária para adaptar os requerimentos energéticos, melhorar o estado nutricional e prevenir ganho de peso. Calorimetria indireta (CI) é o padrão-ouro para a medição do metabolismo basal. No entanto, ele pode ser estimado utilizando-se métodos alternativos
Are the general equations to predict BMR applicable to patients with anorexia nervosa?
Marra, M; Polito, A; De Filippo, E; Cuzzolaro, M; Ciarapica, D; Contaldo, F; Scalfi, L
2002-03-01
To determine whether the general equations to predict basal metabolic rate (BMR) can be reliably applied to female anorectics. Two hundred and thirty-seven female patients with anorexia nervosa (AN) were divided into an adolescent group [n=43, 13-17 yrs, 39.3+/-5.0 kg, body mass index (BMI) (weight/height) 15.5+/-1.8 kg/m2] and a young-adult group (n=194, 18-40 yrs, 40.5+/-6.1 kg, BMI 15.6+/-1.9 kg/m2). BMR values determined by indirect calorimetry were compared with those predicted according to either the WHO/FAO/UNU or the Harris-Benedict general equations, or using the Schebendach correction formula (proposed for adjusting the Harris-Benedict estimates in anorectics). Measured BMR was 3,658+/-665 kJ/day in the adolescent and 3,907+/-760 kJ/day in the young-adult patients. In the adolescent group, the differences between predicted and measured values were (mean+/-SD) 1,466 529 kJ/day (+44+/-21%) for WHO/FAO/UNU, 1,587+/-552 kJ/day (+47+/-23%) for the Harris-Benedict and -20+/-510 kJ/day for the Schebendach (+1+/-13%), while in the young-adult group the corresponding values were 696+/-570 kJ/day (+24+/-24%), 1,252+/-644 kJ/day (+37+/-27%) and -430+/-640 kJ/day (-9+/-16%). The bias was negatively associated with weight and BMI in both groups when using the WHO/FAO/UNU and Harris-Benedict equations, and with age in the young-adult group for the Harris-Benedict and Schebendach equations. The WHO/FAO/UNU and Harris-Benedict equations greatly overestimate BMR in AN. Accurate estimation is to some extent dependent on individual characteristics such as age, weight or BMI. The Schebendach correction formula accurately predicts BMR in female adolescents, but not in young adult women with AN.
Validity of predictive equations for basal metabolic rate in Japanese adults.
Miyake, Rieko; Tanaka, Shigeho; Ohkawara, Kazunori; Ishikawa-Takata, Kazuko; Hikihara, Yuki; Taguri, Emiko; Kayashita, Jun; Tabata, Izumi
2011-01-01
Many predictive equations for basal metabolic rate (BMR) based on anthropometric measurements, age, and sex have been developed, mainly for healthy Caucasians. However, it has been reported that many of these equations, used widely, overestimate BMR not only for Asians, but also for Caucasians. The present study examined the accuracy of several predictive equations for BMR in Japanese subjects. In 365 healthy Japanese male and female subjects, aged 18 to 79 y, BMR was measured in the post-absorptive state using a mask and Douglas bag. Six predictive equations were examined. Total error was used as an index of the accuracy of each equation's prediction. Predicted BMR values by Dietary Reference Intakes for Japanese (Japan-DRI), Adjusted Dietary Reference Intakes for Japanese (Adjusted-DRI), and Ganpule equations were not significantly different from the measured BMR in either sex. On the other hand, Harris-Benedict, Schofield, and Food and Agriculture Organization of the United Nations/World Health Organization/United Nations University equations were significantly higher than the measured BMR in both sexes. The prediction error by Japan-DRI, Adjusted-DRI, and Harris-Benedict equations was significantly correlated with body weight in both sexes. Total error using the Ganpule equation was low in both males and females (125 and 99 kcal/d, respectively). In addition, total error using the Adjusted-DRI equation was low in females (95 kcal/d). Thus, the Ganpule equation was the most accurate in predicting BMR in our healthy Japanese subjects, because the difference between the predicted and measured BMR was relatively small, and body weight had no effect on the prediction error.
Carla Barbosa Nonino
2002-01-01
Vários estudos analisando a taxa de metabolismo de repouso (TMR) contribuíram com equações cuja proposta era estabelecer padrões que pudessem ser genericamente utilizadas para se estimar a TMR. A equação de Harris-Benedict (HB), permanece como o método mais comumente utilizado para estimar a TMR. Porém, em indivíduos obesos o uso de equações preditivas da TMR pode levar a resultados conflitantes. Indivíduos obesos submetidos a dietas hipocalóricas podem apresentar uma diminuição da TMR e do ...
Henes, Sarah T; Cummings, Doyle M; Hickner, Robert C; Houmard, Joseph A; Kolasa, Kathryn M; Lazorick, Suzanne; Collier, David N
2013-10-01
The Academy of Nutrition and Dietetics recommends the use of indirect calorimetry for calculating caloric targets for weight loss in obese youth. Practitioners typically use predictive equations since indirect calorimetry is often not available. The objective of this study was to compare measured resting energy expenditure (MREE) with that estimated using published predictive equations in obese pediatric patients. Youth aged 7 to 18 years (n = 80) who were referred to a university-based healthy weight clinic and who were greater than the 95th percentile BMI for age and gender participated. MREE was measured via a portable indirect calorimeter. Predicted energy expenditure (pEE) was estimated using published equations including those commonly used in children. pEE was compared to the MREE for each subject. Absolute mean difference between MREE and pEE, mean percentage accuracy, and mean error were determined. Mean percentage accuracy of pEE compared with MREE varied widely, with the Harris-Benedict, Lazzer, and Molnar equations providing the greatest accuracy (65%, 61%, and 60%, respectively). Mean differences between MREE and equation-estimated caloric targets varied from 197.9 kcal/day to 307.7 kcal/day. The potential to either overestimate or underestimate calorie needs in the clinical setting is significant when comparing EE derived from predictive equations with that measured using portable indirect calorimetry. While our findings suggest that the Harris-Benedict equation has improved accuracy relative to other equations in severely obese youth, the potential for error remains sufficiently great to suggest that indirect calorimetry is preferred.
Prediction Equations Overestimate the Energy Requirements More for Obesity-Susceptible Individuals.
McLay-Cooke, Rebecca T; Gray, Andrew R; Jones, Lynnette M; Taylor, Rachael W; Skidmore, Paula M L; Brown, Rachel C
2017-09-13
Predictive equations to estimate resting metabolic rate (RMR) are often used in dietary counseling and by online apps to set energy intake goals for weight loss. It is critical to know whether such equations are appropriate for those susceptible to obesity. We measured RMR by indirect calorimetry after an overnight fast in 26 obesity susceptible (OSI) and 30 obesity resistant (ORI) individuals, identified using a simple 6-item screening tool. Predicted RMR was calculated using the FAO/WHO/UNU (Food and Agricultural Organisation/World Health Organisation/United Nations University), Oxford and Miflin-St Jeor equations. Absolute measured RMR did not differ significantly between OSI versus ORI (6339 vs. 5893 kJ·d -1 , p = 0.313). All three prediction equations over-estimated RMR for both OSI and ORI when measured RMR was ≤5000 kJ·d -1 . For measured RMR ≤7000 kJ·d -1 there was statistically significant evidence that the equations overestimate RMR to a greater extent for those classified as obesity susceptible with biases ranging between around 10% to nearly 30% depending on the equation. The use of prediction equations may overestimate RMR and energy requirements particularly in those who self-identify as being susceptible to obesity, which has implications for effective weight management.
Existing creatinine-based equations overestimate glomerular filtration rate in Indians.
Kumar, Vivek; Yadav, Ashok Kumar; Yasuda, Yoshinari; Horio, Masaru; Kumar, Vinod; Sahni, Nancy; Gupta, Krishan L; Matsuo, Seiichi; Kohli, Harbir Singh; Jha, Vivekanand
2018-02-01
Accurate estimation of glomerular filtration rate (GFR) is important for diagnosis and risk stratification in chronic kidney disease and for selection of living donors. Ethnic differences have required correction factors in the originally developed creatinine-based GFR estimation equations for populations around the world. Existing equations have not been validated in the vegetarian Indian population. We examined the performance of creatinine and cystatin-based GFR estimating equations in Indians. GFR was measured by urinary clearance of inulin. Serum creatinine was measured using IDMS-traceable Jaffe's and enzymatic assays, and cystatin C by colloidal gold immunoassay. Dietary protein intake was calculated by measuring urinary nitrogen appearance. Bias, precision and accuracy were calculated for the eGFR equations. A total of 130 participants (63 healthy kidney donors and 67 with CKD) were studied. About 50% were vegetarians, and the remainder ate meat 3.8 times every month. The average creatinine excretion were 14.7 mg/kg/day (95% CI: 13.5 to 15.9 mg/kg/day) and 12.4 mg/kg/day (95% CI: 11.2 to 13.6 mg/kg/day) in males and females, respectively. The average daily protein intake was 46.1 g/day (95% CI: 43.2 to 48.8 g/day). The mean mGFR in the study population was 51.66 ± 31.68 ml/min/1.73m 2 . All creatinine-based eGFR equations overestimated GFR (p < 0.01 for each creatinine based eGFR equation). However, eGFR by CKD-EPI Cys was not significantly different from mGFR (p = 0.38). The CKD-EPI Cys exhibited lowest bias [mean bias: -3.53 ± 14.70 ml/min/1.73m 2 (95% CI: -0.608 to -0.98)] and highest accuracy (P 30 : 74.6%). The GFR in the healthy population was 79.44 ± 20.19 (range: 41.90-134.50) ml/min/1.73m 2 . Existing creatinine-based GFR estimating equations overestimate GFR in Indians. An appropriately powered study is needed to develop either a correction factor or a new equation for accurate assessment of kidney function in the
First page Back Continue Last page Graphics. Extensive field studies revealed over-estimates of bamboo stocks by a factor of ten! Extensive field studies revealed over-estimates of bamboo stocks by a factor of ten! Forest compartments that had been completely clear felled to set up WCPM still showed large stocks because ...
Souza, Micheline Tereza Pires; Singer, Pierre; Ozorio, Gislaine Aparecida; Rosa, Vitor Modesto; Alves, Maria Manuela Ferreira; Mendoza López, Rossana Verónica; Waitzberg, Dan L
2018-02-05
Patients with head and neck cancer have changes in body composition and resting energy expenditure (REE) related to significant inflammatory processes. We investigated REE and body composition in a population of patients with head and neck cancer, comparing the measured REE with predicted energy expenditure and deriving an equation of anthropometric values and body composition. This retrospective, observational, descriptive study of a single center included patients with head and neck cancer. We evaluated nutritional status by body mass index (BMI) and Patient-Generated Subjective Global Assessment (PG-SGA), body composition by electric bioimpedance, and REE by indirect calorimetry (IC). We included 140 patients, most of whom were men (80.7%), 60 y or older (58.6%), and had advanced disease (77.9%). Most were malnourished by BMI standards (77.9%) and severely malnourished according to the PG-SGA (49.3%), with a fat-free mass below the ideal values (82.9%) associated with sarcopenia (92.1%). Hypermetabolism was 57%. When comparing REE with the Harris-Benedict formula, we found the agreement limits from -546 613 to 240 708, the mean difference was -152 953 (95% confidence interval [CI], -185 844 to -120 062) and Pitman's variance test was r = -0.294 (P = 0.001). When we included the activity factor and the thermogenesis factor in REE and compared with Harris-Benedict, we found the agreement limits from -764.423 to 337.087, a mean difference of -213.668 (95% CI -259.684 to -167.652), and the Pitman's variance text at r = -0.292 (P = 0.001). Predictive equations, generally recommended by guidelines, are imprecise when compared with IC measures. Therefore, we suggest a new predictive equation. Copyright © 2018 Elsevier Inc. All rights reserved.
Resting Energy Expenditure in Anorexia Nervosa: Measured versus Estimated
Marwan El Ghoch
2012-01-01
Full Text Available Introduction. Aim of this study was to compare the resting energy expenditure (REE measured by the Douglas bag method with the REE estimated with the FitMate method, the Harris-Benedict equation, and the Müller et al. equation for individuals with BMI < 18.5 kg/m2 in a severe group of underweight patients with anorexia nervosa (AN. Methods. 15 subjects with AN participated in the study. The Douglas bag method and the FitMate method were used to measure REE and the dual energy X-ray absorptiometry to assess body composition after one day of refeeding. Results. FitMate method and the Müller et al. equation gave an accurate REE estimation, while the Harris-Benedict equation overestimated the REE when compared with the Douglas bag method. Conclusion. The data support the use of the FitMate method and the Müller et al. equation, but not the Harris-Benedict equation, to estimate REE in AN patients after short-term refeeding.
Dowling, Thomas C; Wang, En-Shih; Ferrucci, Luigi; Sorkin, John D
2013-09-01
To evaluate the performance of kidney function estimation equations and to determine the frequency of drug dose discordance in an older population. Cross-sectional analysis of data from community-dwelling volunteers randomly selected from the Baltimore Longitudinal Study of Aging from January 1, 2005, to December 31, 2010. A total of 269 men and women with a mean ± SD age of 81 ± 6 years, mean serum creatinine concentration (Scr ) of 1.1 ± 0.4 mg/dl, and mean 24-hour measured creatinine clearance (mClcr ) of 53 ± 13 ml/minute. Kidney function was estimated by using the following equations: Cockcroft-Gault (CG), Modification of Diet in Renal Disease (MDRD), and Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI). The performance of each equation was assessed by measuring bias and precision relative to mClcr . Dose calculation errors (discordance) were determined for 10 drugs requiring renal dosage adjustments to avoid toxicity when compared with the dosages approved by the Food and Drug Administration. The CG equation was the least biased estimate of mClcr . The MDRD and CKD-EPI equations were significantly positively biased compared with CG (mean ± SD 34 ± 20% and 22 ± 15%, respectively, prenal impairment. Thus equations estimating glomerular filtration rate should not be substituted in place of the CG equation in older adults for the purpose of renal dosage adjustments. In addition, the common practice of rounding or replacing low Scr values with an arbitrary value of 1.0 mg/dl for use in the CG equation should be avoided. Additional studies that evaluate alternative eGFR equations in the older populations that incorporate pharmacokinetic and pharmacodynamic outcomes measures are needed. © 2013 Pharmacotherapy Publications, Inc.
Achamrah, Najate; Jésus, Pierre; Grigioni, Sébastien; Rimbert, Agnès; Petit, André; Déchelotte, Pierre; Folope, Vanessa; Coëffier, Moïse
2018-01-01
Predictive equations have been specifically developed for obese patients to estimate resting energy expenditure (REE). Body composition (BC) assessment is needed for some of these equations. We assessed the impact of BC methods on the accuracy of specific predictive equations developed in obese patients. REE was measured (mREE) by indirect calorimetry and BC assessed by bioelectrical impedance analysis (BIA) and dual-energy X-ray absorptiometry (DXA). mREE, percentages of prediction accuracy (±10% of mREE) were compared. Predictive equations were studied in 2588 obese patients. Mean mREE was 1788 ± 6.3 kcal/24 h. Only the Müller (BIA) and Harris & Benedict (HB) equations provided REE with no difference from mREE. The Huang, Müller, Horie-Waitzberg, and HB formulas provided a higher accurate prediction (>60% of cases). The use of BIA provided better predictions of REE than DXA for the Huang and Müller equations. Inversely, the Horie-Waitzberg and Lazzer formulas provided a higher accuracy using DXA. Accuracy decreased when applied to patients with BMI ≥ 40, except for the Horie-Waitzberg and Lazzer (DXA) formulas. Müller equations based on BIA provided a marked improvement of REE prediction accuracy than equations not based on BC. The interest of BC to improve REE predictive equations accuracy in obese patients should be confirmed. PMID:29320432
Xiao, Guizhen; Xie, Qiuyou; He, Yanbin; Wang, Ziwen; Chen, Yan; Jiang, Mengliu; Ni, Xiaoxiao; Wang, Qinxian; Murong, Min; Guo, Yequn; Qiu, Xiaowen; Yu, Ronghao
2017-10-01
Accurately predicting the basal metabolic rate (BMR) of patients in a vegetative state (VS) or minimally conscious state (MCS) is critical to proper nutritional therapy, but commonly used equations have not been shown to be accurate. Therefore, we compared the BMR measured by indirect calorimetry (IC) to BMR values estimated using common predictive equations in VS and MCS patients. Body composition variables were measured using the bioelectric impedance analysis (BIA) technique. BMR was measured by IC in 82 patients (64 men and 18 women) with VS or MCS. Patients were classified by body mass index as underweight (BMR was estimated for each group using the Harris-Benedict (H-B), Schofield, or Cunningham equations and compared to the measured BMR using Bland-Altman analyses. For the underweight group, there was a significant difference between the measured BMR values and the estimated BMR values calculated using the H-B, Schofield, and Cunningham equations (p BMR values estimated using the H-B and Cunningham equations were different significantly from the measured BMR (p BMR in the normal-weight group. The Schofield equation showed the best concordance (only 41.5%) with the BMR values measured by IC. None of the commonly used equations to estimate BMR were suitable for the VS or MCS populations. Indirect calorimetry is the preferred way to avoid either over or underestimate of BMR values. Copyright © 2016. Published by Elsevier Ltd.
Oliveira, Ben; Sridharan, Sivakumar; Farrington, Ken; Davenport, Andrew
2017-07-13
Waste products of metabolism are retained in haemodialysis (HD) patients. Cellular metabolism generates energy, and patients with greater energy expenditure may therefore require more dialysis. To determine the amount of dialysis required, equations estimating resting and total energy expenditure (REE,TEE) are required. We compared estimates of REE in HD patients using established equations with a novel equation recently validated in HD patients (HD equation). TEE was derived from REE (HD equation) and estimates of physical activity obtained by questionnaire. REE and TEE relationships with bioimpedance measured body composition were then determined. We studied 317 HD patients; 195 males (61.5%), 123 diabetic (38.9%), mean age 65.0 ± 15.3 and weight 73.1 ± 16.8 kg. REE from HD Equation was 1509 ± 241 kcal/day, which was greater than for Mifflin St Joer 1384 ± 259, Harris-Benedict 1437 ± 244, Katch-McArdle 1345 ± 232 (all p employment (β 406.5, p appearance (β 2.7, p = 0.015), and negatively with age (β -7.9, p appearance, lower co-morbidity, age, and dialysis vintage, and the employed. More metabolically active patients may require greater dialytic clearances. This article is protected by copyright. All rights reserved.
Spears, Karen E; Kim, Hyunsook; Behall, Kay M; Conway, Joan M
2009-05-01
To compare standardized prediction equations to a hand-held indirect calorimeter in estimating resting energy and total energy requirements in overweight women. Resting energy expenditure (REE) was measured by hand-held indirect calorimeter and calculated by prediction equations Harris-Benedict, Mifflin-St Jeor, World Health Organization/Food and Agriculture Organization/United Nations University (WHO), and Dietary Reference Intakes (DRI). Physical activity level, assessed by questionnaire, was used to estimate total energy expenditure (TEE). Subjects (n=39) were female nonsmokers older than 25 years of age with body mass index more than 25. Repeated measures analysis of variance, Bland-Altman plot, and fitted regression line of difference. A difference within +/-10% of two methods indicated agreement. Significant proportional bias was present between hand-held indirect calorimeter and prediction equations for REE and TEE (Pvalues and underestimated at higher values. Mean differences (+/-standard error) for REE and TEE between hand-held indirect calorimeter and Harris-Benedict were -5.98+/-46.7 kcal/day (P=0.90) and 21.40+/-75.7 kcal/day (P=0.78); between hand-held indirect calorimeter and Mifflin-St Jeor were 69.93+/-46.7 kcal/day (P=0.14) and 116.44+/-75.9 kcal/day (P=0.13); between hand-held indirect calorimeter and WHO were -22.03+/-48.4 kcal/day (P=0.65) and -15.8+/-77.9 kcal/day (P=0.84); and between hand-held indirect calorimeter and DRI were 39.65+/-47.4 kcal/day (P=0.41) and 56.36+/-85.5 kcal/day (P=0.51). Less than 50% of predictive equation values were within +/-10% of hand-held indirect calorimeter values, indicating poor agreement. A significant discrepancy between predicted and measured energy expenditure was observed. Further evaluation of hand-held indirect calorimeter research screening is needed.
ten Haaf, Twan; Weijs, Peter J M
2014-01-01
Resting energy expenditure (REE) is expected to be higher in athletes because of their relatively high fat free mass (FFM). Therefore, REE predictive equation for recreational athletes may be required. The aim of this study was to validate existing REE predictive equations and to develop a new recreational athlete specific equation. 90 (53 M, 37 F) adult athletes, exercising on average 9.1 ± 5.0 hours a week and 5.0 ± 1.8 times a week, were included. REE was measured using indirect calorimetry (Vmax Encore n29), FFM and FM were measured using air displacement plethysmography. Multiple linear regression analysis was used to develop a new FFM-based and weight-based REE predictive equation. The percentage accurate predictions (within 10% of measured REE), percentage bias, root mean square error and limits of agreement were calculated. Results: The Cunningham equation and the new weight-based equation REE(kJ / d) = 49.940* weight(kg) + 2459.053* height(m) - 34.014* age(y) + 799.257* sex(M = 1,F = 0) + 122.502 and the new FFM-based equation REE(kJ / d) = 95.272*FFM(kg) + 2026.161 performed equally well. De Lorenzo's equation predicted REE less accurate, but better than the other generally used REE predictive equations. Harris-Benedict, WHO, Schofield, Mifflin and Owen all showed less than 50% accuracy. For a population of (Dutch) recreational athletes, the REE can accurately be predicted with the existing Cunningham equation. Since body composition measurement is not always possible, and other generally used equations fail, the new weight-based equation is advised for use in sports nutrition.
Comparison of different methods to estimate BMR in adoloscent student population.
Patil, Suchitra R; Bharadwaj, Jyoti
2011-01-01
There is a growing clinical emphasis for the measurement of BMR and energy expenditure in clinical and research investigation such as obesity, exercise, cancer, under-nutrition, trauma and infections. Hence, there is a motivation towards calculating basal metabolic rate using standard equations. The objective of the present work is to identify an appropriate equation in Indian environment for the estimation of calorie needs and basal metabolic rate using the measured height, weight, age and skin fold parameters of an individual. Basal metabolic rates of adolescent male and female population aged between 17-20 years were estimated using equations proposed by FAO, ICMR, Cunningham, Harris Benedict, Fredrix and Miffin. Calorie needs were calculated using factorial approach which involves the multiplication of basal metabolic rate with appropriate physical activity factor. Basal metabolic rates estimated by FAO, Cunningham, Harris-Benedict, Fredrix and Miffin are reduced by 5%. These reduced basal metabolic rates and calorie needs are compared with that obtained by Cunningham's equation which is considered as accurate equation. Comparison of the basal metabolic rates and calorie needs obtained by Cunningham equation with all equations such as Harris-Benedict, FAO, Fredrix and Miffin after 5% reduction and ICMR equation without reduction indicates that Harris-Benedict, Fredrix, Miffin and FAO equations can be used for male and female adolescent populations for Indian environment. In conclusion, Harris-Benedict equation is an appropriate equation for both male and female adolescent population for Indian environment.
Paula Guedes Cocate
2009-10-01
Full Text Available A taxa metabólica de repouso (TMR pode ser determinada por calorimetria indireta (CI. Porém, em função da praticidade, na prática clínica na maioria das vezes esta é estimada por equações de predição, as quais foram desenvolvidas em estudos envolvendo indivíduos não atletas. Apesar de alguns autores terem indicado que tais equações não estimam adequadamente a TMR, estas têm sido bastante utilizadas para calculá-la e prescrever dietas, inclusive para atletas. O objetivo deste estudo foi comparar a TMR determinada por CI com a estimada pelas equações de Harris & Benedict (HB, Schofield, FAO/WHO/UNU e Henry & Rees (HR, em 15 homens ciclistas, de 24,4 ± 3,68 anos, apresentando índice de massa corporal de 21,97 ± 1,46kg/m² e VO2máx de 70,00 ± 5,32mL(kg.min-1. Para comparar a TMR determinada por CI e pelas equações, utilizou-se o tratamento estatístico testes t de Student (variáveis com distribuição normal e de Mann-Whitney (variáveis sem distribuição normal, considerando p The resting metabolic rate (RMR can be determined by indirect calorimetry (IC. However, the clinical estimation of this parameter has been done using mathematical equations, which were developed in studies involving non-athletes. Although some authors have indicated that such equations do not estimate correctly the RMR, they have been constantly used to estimate such parameter and to prescribe diets, including for athletes. The objective of this study was to compare the RMR determined by IC with the ones estimated using the equations proposed by Harris & Benedict (HB, Schofield, FAO/WHO/UNU and Henry & Rees (HR, in 15 male cyclists, aged 24.4±3.68 years, body mass index of 21.97±1.46 kg/m² and VO2max of 70.00±5.32 mL(kg.min-1. Student's t test (when data presented normal distribution and Mann-Whitney (when data did not present normal distribution were used to compare the RMR determined by IC and the ones estimated by the equations. Probability
Staal, Sarah; Sjödin, Anders; Fahrenholtz, Ida; Bonnesen, Karen; Melin, Anna Katarina
2018-06-22
Ballet dancers are reported to have an increased risk for energy deficiency with or without disordered eating behavior. A low ratio between measured ( m ) and predicted ( p ) resting metabolic rate (RMR ratio energy deficiency. We aimed to evaluate the prevalence of suppressed RMR using different methods to calculate p RMR and to explore associations with additional markers of energy deficiency. Female (n = 20) and male (n = 20) professional ballet dancers, 19-35 years of age, were enrolled. m RMR was assessed by respiratory calorimetry (ventilated open hood). p RMR was determined using the Cunningham and Harris-Benedict equations, and different tissue compartments derived from whole-body dual-energy X-ray absorptiometry assessment. The protocol further included assessment of body composition and bone mineral density, blood pressure, disordered eating (Eating Disorder Inventory-3), and for females, the Low Energy Availability in Females Questionnaire. The prevalence of suppressed RMR was generally high but also clearly dependent on the method used to calculate p RMR, ranging from 25% to 80% in males and 35% to 100% in females. Five percent had low bone mineral density, whereas 10% had disordered eating and 25% had hypotension. Forty percent of females had elevated Low Energy Availability in Females Questionnaire score and 50% were underweight. Suppressed RMR was associated with elevated Low Energy Availability in Females Questionnaire score in females and with higher training volume in males. In conclusion, professional ballet dancers are at risk for energy deficiency. The number of identified dancers at risk varies greatly depending on the method used to predict RMR when using RMR ratio as a marker for energy deficiency.
Overestimating resource value and its effects on fighting decisions.
Lee Alan Dugatkin
Full Text Available Much work in behavioral ecology has shown that animals fight over resources such as food, and that they make strategic decisions about when to engage in such fights. Here, we examine the evolution of one, heretofore unexamined, component of that strategic decision about whether to fight for a resource. We present the results of a computer simulation that examined the evolution of over- or underestimating the value of a resource (food as a function of an individual's current hunger level. In our model, animals fought for food when they perceived their current food level to be below the mean for the environment. We considered seven strategies for estimating food value: 1 always underestimate food value, 2 always overestimate food value, 3 never over- or underestimate food value, 4 overestimate food value when hungry, 5 underestimate food value when hungry, 6 overestimate food value when relatively satiated, and 7 underestimate food value when relatively satiated. We first competed all seven strategies against each other when they began at approximately equal frequencies. In such a competition, two strategies--"always overestimate food value," and "overestimate food value when hungry"--were very successful. We next competed each of these strategies against the default strategy of "never over- or underestimate," when the default strategy was set at 99% of the population. Again, the strategies of "always overestimate food value" and "overestimate food value when hungry" fared well. Our results suggest that overestimating food value when deciding whether to fight should be favored by natural selection.
Predictive Validity of Explicit and Implicit Threat Overestimation in Contamination Fear
Green, Jennifer S.; Teachman, Bethany A.
2012-01-01
We examined the predictive validity of explicit and implicit measures of threat overestimation in relation to contamination-fear outcomes using structural equation modeling. Undergraduate students high in contamination fear (N = 56) completed explicit measures of contamination threat likelihood and severity, as well as looming vulnerability cognitions, in addition to an implicit measure of danger associations with potential contaminants. Participants also completed measures of contamination-fear symptoms, as well as subjective distress and avoidance during a behavioral avoidance task, and state looming vulnerability cognitions during an exposure task. The latent explicit (but not implicit) threat overestimation variable was a significant and unique predictor of contamination fear symptoms and self-reported affective and cognitive facets of contamination fear. On the contrary, the implicit (but not explicit) latent measure predicted behavioral avoidance (at the level of a trend). Results are discussed in terms of differential predictive validity of implicit versus explicit markers of threat processing and multiple fear response systems. PMID:24073390
Reducing WCET Overestimations by Correcting Errors in Loop Bound Constraints
Fanqi Meng
2017-12-01
Full Text Available In order to reduce overestimations of worst-case execution time (WCET, in this article, we firstly report a kind of specific WCET overestimation caused by non-orthogonal nested loops. Then, we propose a novel correction approach which has three basic steps. The first step is to locate the worst-case execution path (WCEP in the control flow graph and then map it onto source code. The second step is to identify non-orthogonal nested loops from the WCEP by means of an abstract syntax tree. The last step is to recursively calculate the WCET errors caused by the loose loop bound constraints, and then subtract the total errors from the overestimations. The novelty lies in the fact that the WCET correction is only conducted on the non-branching part of WCEP, thus avoiding potential safety risks caused by possible WCEP switches. Experimental results show that our approach reduces the specific WCET overestimation by an average of more than 82%, and 100% of corrected WCET is no less than the actual WCET. Thus, our approach is not only effective but also safe. It will help developers to design energy-efficient and safe real-time systems.
Overestimation of Knowledge about Word Meanings: The "Misplaced Meaning" Effect
Kominsky, Jonathan F.; Keil, Frank C.
2014-01-01
Children and adults may not realize how much they depend on external sources in understanding word meanings. Four experiments investigated the existence and developmental course of a "Misplaced Meaning" (MM) effect, wherein children and adults overestimate their knowledge about the meanings of various words by underestimating how much…
Do young novice drivers overestimate their driving skills?
Craen, S. de Twisk, D.A.M. Hagenzieker, M.P. Elffers, H. & Brookhuis, K.A.
2007-01-01
In this study the authors argue that, in order to sufficiently adapt to task demands in traffic, drivers have to make an assessment of their own driving skills. There are indications that drivers in general, and novice drivers in particular, overestimate their driving skills. The objective of this
Gniewosz, Burkhard; Watt, Helen M G
2017-07-01
This study examines whether and how student-perceived parents' and teachers' overestimation of students' own perceived mathematical ability can explain trajectories for adolescents' mathematical task values (intrinsic and utility) controlling for measured achievement, following expectancy-value and self-determination theories. Longitudinal data come from a 3-cohort (mean ages 13.25, 12.36, and 14.41 years; Grades 7-10), 4-wave data set of 1,271 Australian secondary school students. Longitudinal structural equation models revealed positive effects of student-perceived overestimation of math ability by parents and teachers on students' intrinsic and utility math task values development. Perceived parental overestimations predicted intrinsic task value changes between all measurement occasions, whereas utility task value changes only were predicted between Grades 9 and 10. Parental influences were stronger for intrinsic than utility task values. Teacher influences were similar for both forms of task values and commenced after the curricular school transition in Grade 8. Results support the assumptions that the perceived encouragement conveyed by student-perceived mathematical ability beliefs of parents and teachers, promote positive mathematics task values development. Moreover, results point to different mechanisms underlying parents' and teachers' support. Finally, the longitudinal changes indicate transition-related increases in the effects of student-perceived overestimations and stronger effects for intrinsic than utility values. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
MRI Overestimates Excitotoxic Amygdala Lesion Damage in Rhesus Monkeys
Benjamin M. Basile
2017-06-01
Full Text Available Selective, fiber-sparing excitotoxic lesions are a state-of-the-art tool for determining the causal contributions of different brain areas to behavior. For nonhuman primates especially, it is advantageous to keep subjects with high-quality lesions alive and contributing to science for many years. However, this requires the ability to estimate lesion extent accurately. Previous research has shown that in vivo T2-weighted magnetic resonance imaging (MRI accurately estimates damage following selective ibotenic acid lesions of the hippocampus. Here, we show that the same does not apply to lesions of the amygdala. Across 19 hemispheres from 13 rhesus monkeys, MRI assessment consistently overestimated amygdala damage as assessed by microscopic examination of Nissl-stained histological material. Two outliers suggested a linear relation for lower damage levels, and values of unintended amygdala damage from a previous study fell directly on that regression line, demonstrating that T2 hypersignal accurately predicts damage levels below 50%. For unintended damage, MRI estimates correlated with histological assessment for entorhinal cortex, perirhinal cortex and hippocampus, though MRI significantly overestimated the extent of that damage in all structures. Nevertheless, ibotenic acid injections routinely produced extensive intentional amygdala damage with minimal unintended damage to surrounding structures, validating the general success of the technique. The field will benefit from more research into in vivo lesion assessment techniques, and additional evaluation of the accuracy of MRI assessment in different brain areas. For now, in vivo MRI assessment of ibotenic acid lesions of the amygdala can be used to confirm successful injections, but MRI estimates of lesion extent should be interpreted with caution.
Sundström, Martin; Mehrabi, Mahboubeh; Tjäder, Inga; Rooyackers, Olav; Hammarqvist, Folke
2017-08-01
Indirect calorimetry (IC) is the gold standard for determining energy expenditure in patients requiring mechanical ventilation. Metabolic armbands using data derived from dermal measurements have been proposed as an alternative to IC in healthy subjects, but their utility during critical illness is unclear. The aim of this study was to determine the level of agreement between the SenseWear armband and the Deltatrac Metabolic Monitor in mechanically ventilated intensive care unit (ICU) patients. Adult ICU patients requiring invasive ventilator therapy were eligible for inclusion. Simultaneous measurements were performed with the SenseWear Armband and Deltatrac under stable conditions. Resting energy expenditure (REE) values were registered for both instruments and compared with Bland-Altman plots. Forty-two measurements were performed in 30 patients. The SenseWear Armband measured significantly higher REE values as compared with IC (mean bias, 85 kcal/24 h; P = .027). Less variability was noted between individual SenseWear measurements and REE as predicted by the Harris-Benedict equation (2 SD, ±327 kcal/24 h) than when IC was compared with SenseWear and Harris-Benedict (2 SD, ±473 and ±543 kcal/24 h, respectively). The systematic bias and large variability of the SenseWear armband when compared with gas exchange measurements confer limited benefits over the Harris Benedict equation in determining caloric requirements of ICU patients.
Kork, F; Balzer, F; Krannich, A; Bernardi, M H; Eltzschig, H K; Jankowski, J; Spies, C
2017-03-01
Acute kidney injury (AKI) is diagnosed by a 50% increase in creatinine. For patients without a baseline creatinine measurement, guidelines suggest estimating baseline creatinine by back-calculation. The aim of this study was to evaluate different glomerular filtration rate (GFR) equations and different GFR assumptions for back-calculating baseline creatinine as well as the effect on the diagnosis of AKI. The Modification of Diet in Renal Disease, the Chronic Kidney Disease Epidemiology (CKD-EPI) and the Mayo quadratic (MQ) equation were evaluated to estimate baseline creatinine, each under the assumption of either a fixed GFR of 75 mL min -1 1.73 m -2 or an age-adjusted GFR. Estimated baseline creatinine, diagnoses and severity stages of AKI based on estimated baseline creatinine were compared to measured baseline creatinine and corresponding diagnoses and severity stages of AKI. The data of 34 690 surgical patients were analysed. Estimating baseline creatinine overestimated baseline creatinine. Diagnosing AKI based on estimated baseline creatinine had only substantial agreement with AKI diagnoses based on measured baseline creatinine [Cohen's κ ranging from 0.66 (95% CI 0.65-0.68) to 0.77 (95% CI 0.76-0.79)] and overestimated AKI prevalence with fair sensitivity [ranging from 74.3% (95% CI 72.3-76.2) to 90.1% (95% CI 88.6-92.1)]. Staging AKI severity based on estimated baseline creatinine had moderate agreement with AKI severity based on measured baseline creatinine [Cohen's κ ranging from 0.43 (95% CI 0.42-0.44) to 0.53 (95% CI 0.51-0.55)]. Diagnosing AKI and staging AKI severity on the basis of estimated baseline creatinine in surgical patients is not feasible. Patients at risk for post-operative AKI should have a pre-operative creatinine measurement to adequately assess post-operative AKI. © 2016 Scandinavian Physiological Society. Published by John Wiley & Sons Ltd.
Have We Overestimated Saline Aquifer CO2 Storage Capacities?
Thibeau, S.; Mucha, V.
2011-01-01
approach, it is applied to the Utsira aquifer in the North Sea. In Sections 3 and 4, we discuss possible effects that may lead to higher or lower CO 2 storage efficiencies. Water production appears to be an attractive strategy in order to address regional scale pressure build up and, consequently, to increase the storage capacity. Following these quantitative applications, we recommend to evaluate the CO 2 storage capacities of an aquifer, during a screening study for ranking purposes, using a pressure and compressibility formula rather than a volumetric approach, in order to avoid large overestimation of the aquifer storage capacity. Further studies are naturally required to validate the storage capacities at a qualification stage. (authors)
Gun Carrying by High School Students in Boston, MA: Does Overestimation of Peer Gun Carrying Matter?
Hemenway, David; Vriniotis, Mary; Johnson, Renee M.; Miller, Matthew; Azrael, Deborah
2011-01-01
This paper investigates: (1) whether high school students overestimate gun carrying by their peers, and (2) whether those students who overestimate peer gun carrying are more likely to carry firearms. Data come from a randomly sampled survey conducted in 2008 of over 1700 high school students in Boston, MA. Over 5% of students reported carrying a…
Americans Still Overestimate Social Class Mobility: A Pre-Registered Self-Replication.
Kraus, Michael W
2015-01-01
Kraus and Tan (2015) hypothesized that Americans tend to overestimate social class mobility in society, and do so because they seek to protect the self. This paper reports a pre-registered exact replication of Study 3 from this original paper and finds, consistent with the original study, that Americans substantially overestimate social class mobility, that people provide greater overestimates when made while thinking of similar others, and that high perceived social class is related to greater overestimates. The current results provide additional evidence consistent with the idea that people overestimate class mobility to protect their beliefs in the promise of equality of opportunity. Discussion considers the utility of pre-registered self-replications as one tool for encouraging replication efforts and assessing the robustness of effect sizes.
Americans Still Overestimate Social Class Mobility: A Pre-Registered Self-Replication
Michael W. Kraus
2015-11-01
Full Text Available Kraus and Tan (2015 hypothesized that Americans tend to overestimate social class mobility in society, and do so because they seek to protect the self. This paper reports a pre-registered exact replication of Study 3 from this original paper and finds, consistent with the original study, that Americans substantially overestimate social class mobility, that people provide greater overestimates when made while thinking of similar others, and that high perceived social class is related to greater overestimates. The current results provide additional evidence consistent with the idea that people overestimate class mobility to protect their beliefs in the promise of equality of opportunity. Discussion considers the utility of pre-registered self-replications as one tool for encouraging replication efforts and assessing the robustness of effect sizes.
Swords, Douglas S; Hadley, Edmund D; Swett, Katrina R; Pranikoff, Thomas
2015-01-01
Total body surface area (TBSA) burned is a powerful descriptor of burn severity and influences the volume of resuscitation required in burn patients. The incidence and severity of TBSA overestimation by referring institutions (RIs) in children transferred to a burn center (BC) are unclear. The association between TBSA overestimation and overresuscitation is unknown as is that between TBSA overestimation and outcome. The trauma registry at a BC was queried over 7.25 years for children presenting with burns. TBSA estimate at RIs and BC, total fluid volume given before arrival at a BC, demographic variables, and clinical variables were reviewed. Nearly 20 per cent of children arrived from RIs without TBSA estimation. Nearly 50 per cent were overestimated by 5 per cent or greater TBSA and burn sizes were overestimated by up to 44 per cent TBSA. Average TBSA measured at BC was 9.5 ± 8.3 per cent compared with 15.5 ± 11.8 per cent as measured at RIs (P < 0.0001). Burns between 10 and 19.9 per cent TBSA were overestimated most often and by the greatest amounts. There was a statistically significant relationship between overestimation of TBSA by 5 per cent or greater and overresuscitation by 10 mL/kg or greater (P = 0.02). No patient demographic or clinical factors were associated with TBSA overestimation. Education efforts aimed at emergency department physicians regarding the importance of always calculating TBSA as well as the mechanics of TBSA estimation and calculating resuscitation volume are needed. Further studies should evaluate the association of TBSA overestimation by RIs with adverse outcomes and complications in the burned child.
Kim, Mok Hee; Kim, Yun Hyeon; Choi, Song; Seon, Hyun Ju; Jeong, Gwang Woo; Park, Jin Gyoon; Kang, Heoung Keun; Ko, Joon Seok
2010-01-01
To assess the influence of calcified plaque characteristics on the overestimation of coronary arterial stenosis on a coronary CT angiography (CCTA). The study included 271 coronary arteries with calcified plaques identified by CCTA, and based on 928 coronary arteries from 232 patients who underwent both CCTA and invasive coronary angiography (ICA). Individual coronary arteries were classified into two groups by agreement based on the degree of stenosis from each CCTA and ICA: 1) group A includes patients with concordant CCTA and ICA results and, 2) group B includes patients with an overestimation of CCTA compared to ICA. Parameters including total calcium score, calcium score of an individual coronary artery, calcium burden number of an individual coronary artery, and the density of each calcified plaque (calcium score / number of calcium burden) for each individual coronary artery were compared between the two groups. Of the 271 coronary arteries, 164 (60.5%) were overestimated on CCTA. The left anterior descending artery (LAD) had a significantly low rate of overestimation (47.1%) compared to the other coronary arteries (p=0.001). No significant differences for total calcium score, calcium score of individual coronary artery, and the density of each calcified plaque from individual coronary arteries between two groups was observed. However, a decreasing tendency for the rate of overestimation on CCTA was observed with an increase in calcium burden of individual coronary arteries (p<0.05). The evaluation of coronary arteries suggests that the degree of coronary arterial stenosis had a tendency to be overestimated by calcified plaques on CCTA. However, the rate of overestimation for the degree of coronary arterial stenosis by calcified plaques was not significantly influenced by total calcium score, calcium score of individual coronary artery, and density of each calcified plaque
Tully, Stephanie; Meyvis, Tom
2017-12-01
People value experiences in part because of the memories they create. Yet, we find that people systematically overestimate how much they will retrospect about their experiences. This overestimation results from people focusing on their desire to retrospect about experiences, while failing to consider the experience's limited enduring accessibility in memory. Consistent with this view, we find that desirability is a stronger predictor of forecasted retrospection than it is of reported retrospection, resulting in greater overestimation when the desirability of retrospection is higher. Importantly, the desire to retrospect does not change over time. Instead, past experiences become less top-of-mind over time and, as a result, people simply forget to remember. In line with this account, our results show that obtaining physical reminders of an experience reduces the overestimation of retrospection by increasing how much people retrospect, bringing their realized retrospection more in line with their forecasts (and aspirations). We further observe that the extent to which reported retrospection falls short of forecasted retrospection reliably predicts declining satisfaction with an experience over time. Despite this potential negative consequence of retrospection falling short of expectations, we suggest that the initial overestimation itself may in fact be adaptive. This possibility and other potential implications of this work are discussed. (PsycINFO Database Record (c) 2017 APA, all rights reserved).
"Cool" Topic: Feeding During Moderate Hypothermia After Intracranial Hemorrhage.
Dobak, Stephanie; Rincon, Fred
2017-09-01
Therapeutic moderate hypothermia (MH; T core 33°C-34°C) is being studied for treatment of spontaneous intracerebral hemorrhage (ICH). Nutrition assessment begins with accurate basal metabolic rate (BMR) determination. Although early enteral nutrition (EN) is associated with improved outcomes, it is often deferred until rewarming. We sought to determine the accuracy of predictive BMR equations and the safety and tolerance of EN during MH after ICH. Patients were randomized to 72 hours of MH or normothermia (NT; T core 36°C-37°C). Harris-Benedict (BMR-HB) and Penn-State equation (BMR-PS) calculations were compared with indirect calorimetry (IC) at day (D) 0 and D1-3. Patients with MH received trophic semi-elemental gastric EN. Occurrences of feeding intolerance, gastrointestinal (GI)-related adverse events, and ventilator-associated pneumonia (VAP) were analyzed with a double-sided matched pairs t test. Thirteen patients with ICH participated (6 MH, 7 NT). Mean time to initiate EN: 29.9 (MH) vs 18.4 (NT) hours ( P = .046). Average daily EN calories received D0-3: 398 (MH) vs 1006 (NT) ( P BMR-HB remained stable (1331 kcal), BMR-PS decreased (1511 vs 1145 kcal, P = .5), and IC decreased (1413 vs 985 kcal, P = .2). In patients with ICH undergoing MH, resting energy expenditure is decreased and predictive equations overestimate BMR. EN is feasible, although delayed EN initiation, high gastric residuals, and less EN provision are common. Future studies should focus on EN initiation within 24 hours, advanced EN rates, and postpyloric feeds during hypothermia.
Lake Wobegon’s Guns: Overestimating Our Gun-Related Competences
Emily Stark
2016-02-01
Full Text Available The Lake Wobegon Effect is a general tendency for people to overestimate their own abilities. In this study, the authors conducted a large, nationally-representative survey of U.S. citizens to test whether Americans overestimate their own gun-relevant personality traits, gun safety knowledge, and ability to use a gun in an emergency. The authors also tested how gun control attitudes, political identification, gender, and gun experience affect self-perceptions. Consistent with prior research on the Lake Wobegon Effect, participants overestimated their gun-related competencies. Conservatives, males, and pro-gun advocates self-enhanced somewhat more than their counterparts but this effect was primarily due to increased gun experience among these participants. These findings are important to policymakers in the area of gun use, because overconfidence in one’s gun-related abilities may lead to a reduced perceived need for gun training.
The Validity of Conscientiousness Is Overestimated in the Prediction of Job Performance.
Kepes, Sven; McDaniel, Michael A
2015-01-01
Sensitivity analyses refer to investigations of the degree to which the results of a meta-analysis remain stable when conditions of the data or the analysis change. To the extent that results remain stable, one can refer to them as robust. Sensitivity analyses are rarely conducted in the organizational science literature. Despite conscientiousness being a valued predictor in employment selection, sensitivity analyses have not been conducted with respect to meta-analytic estimates of the correlation (i.e., validity) between conscientiousness and job performance. To address this deficiency, we reanalyzed the largest collection of conscientiousness validity data in the personnel selection literature and conducted a variety of sensitivity analyses. Publication bias analyses demonstrated that the validity of conscientiousness is moderately overestimated (by around 30%; a correlation difference of about .06). The misestimation of the validity appears to be due primarily to suppression of small effects sizes in the journal literature. These inflated validity estimates result in an overestimate of the dollar utility of personnel selection by millions of dollars and should be of considerable concern for organizations. The fields of management and applied psychology seldom conduct sensitivity analyses. Through the use of sensitivity analyses, this paper documents that the existing literature overestimates the validity of conscientiousness in the prediction of job performance. Our data show that effect sizes from journal articles are largely responsible for this overestimation.
Peer substance use overestimation among French university students: a cross-sectional survey
Dautzenberg Bertrand
2010-03-01
Full Text Available Abstract Background Normative misperceptions have been widely documented for alcohol use among U.S. college students. There is less research on other substances or European cultural contexts. This study explores which factors are associated with alcohol, tobacco and cannabis use misperceptions among French college students, focusing on substance use. Methods 12 classes of second-year college students (n = 731 in sociology, medicine, nursing or foreign language estimated the proportion of tobacco, cannabis, alcohol use and heavy episodic drinking among their peers and reported their own use. Results Peer substance use overestimation frequency was 84% for tobacco, 55% for cannabis, 37% for alcohol and 56% for heavy episodic drinking. Cannabis users (p = 0.006, alcohol (p = 0.003 and heavy episodic drinkers (p = 0.002, are more likely to overestimate the prevalence of use of these consumptions. Tobacco users are less likely to overestimate peer prevalence of smoking (p = 0.044. Women are more likely to overestimate tobacco (p Conclusions Local interventions that focus on creating realistic perceptions of substance use prevalence could be considered for cannabis and alcohol prevention in French campuses.
Can we rely on predicted basal metabolic rate in chronic pancreatitis outpatients?
Olesen, Søren Schou; Holst, Mette; Køhler, Marianne; Drewes, Asbjørn Mohr; Rasmussen, Henrik Højgaard
2015-04-01
Malnutrition is a common complication to chronic pancreatitis (CP) and many patients need nutritional support. An accurate estimation of the basal metabolic rate (BMR) is essential when appropriate nutritional support is to be initiated, but in the clinical settings BMR is cumbersome to measure. We therefore investigated whether BMR can be reliable predicted from a standard formula (the Harris-Benedict equation) in CP outpatients. Twenty-eight patients with clinical stable CP and no current alcohol abuse were enrolled. Patients were stratified according to nutritional risk using the Nutrition Risk Screening 2002 system. Body composition was estimated using bioelectrical impedance. BMR was measured using indirect calorimetry and predicted using the Harris-Benedict equation based on anthropometric data. The average predicted BMR was 1371 ± 216 kcal/day compared to an average measured BMR of 1399 ± 231 kcal/day (P = 0.4). The corresponding limits of agreement were -347 to 290 kcal/day. Twenty-two patients (79%) had a measured BMR between 85 and 115% of the predicted BMR. When analysing patients stratified according to nutritional risk profiles, no differences between predicted and measured BMR were evident for any of the risk profile subgroups (all P > 0.2). The BMR was correlated to fat free mass determined by bioelectrical impedance (rho = 0.55; P = 0.003), while no effect modification was seen from nutritional risk stratification in a linear regression analysis (P = 0.4). The Harris-Benedict equation reliable predicts the measured BMR in four out of five clinical stable CP outpatients with no current alcohol abuse. Copyright © 2015 European Society for Clinical Nutrition and Metabolism. Published by Elsevier Ltd. All rights reserved.
Factors associated with overestimation of asthma control: A cross-sectional study in Australia.
Bereznicki, Bonnie J; Chapman, Millicent P; Bereznicki, Luke R E
2017-05-01
To investigate actual and perceived disease control in Australians with asthma, and identify factors associated with overestimation of asthma control. This was a cross-sectional study of Australian adults with asthma, who were recruited via Facebook to complete an online survey. The survey included basic demographic questions, and validated tools assessing asthma knowledge, medication adherence, medicine beliefs, illness perception and asthma control. Items that measured symptoms and frequency of reliever medication use were compared to respondents' self-rating of their own asthma control. Predictors of overestimation of asthma control were determined using multivariate logistic regression. Of 2971 survey responses, 1950 (65.6%) were complete and eligible for inclusion. Overestimation of control was apparent in 45.9% of respondents. Factors independently associated with overestimation of asthma control included education level (OR = 0.755, 95% CI: 0.612-0.931, P = 0.009), asthma knowledge (OR = 0.942, 95% CI: 0.892-0.994, P = 0.029), total asthma control, (OR = 0.842, 95% CI: 0.818-0.867, P addictive (OR = 1.144, 95% CI: 1.017-1.287, P = 0.025), and increased feelings of control over asthma (OR = 1.261, 95% CI: 1.191-1.335), P < 0.001). Overestimation of asthma control remains a significant issue in Australians with asthma. The study highlights the importance of encouraging patients to express their feelings about asthma control and beliefs about medicines, and to be more forthcoming with their asthma symptoms. This would help to reveal any discrepancies between perceived and actual asthma control.
Predictors and overestimation of recalled mobile phone use among children and adolescents.
Aydin, Denis; Feychting, Maria; Schüz, Joachim; Andersen, Tina Veje; Poulsen, Aslak Harbo; Prochazka, Michaela; Klæboe, Lars; Kuehni, Claudia E; Tynes, Tore; Röösli, Martin
2011-12-01
A growing body of literature addresses possible health effects of mobile phone use in children and adolescents by relying on the study participants' retrospective reconstruction of mobile phone use. In this study, we used data from the international case-control study CEFALO to compare self-reported with objectively operator-recorded mobile phone use. The aim of the study was to assess predictors of level of mobile phone use as well as factors that are associated with overestimating own mobile phone use. For cumulative number and duration of calls as well as for time since first subscription we calculated the ratio of self-reported to operator-recorded mobile phone use. We used multiple linear regression models to assess possible predictors of the average number and duration of calls per day and logistic regression models to assess possible predictors of overestimation. The cumulative number and duration of calls as well as the time since first subscription of mobile phones were overestimated on average by the study participants. Likelihood to overestimate number and duration of calls was not significantly different for controls compared to cases (OR=1.1, 95%-CI: 0.5 to 2.5 and OR=1.9, 95%-CI: 0.85 to 4.3, respectively). However, likelihood to overestimate was associated with other health related factors such as age and sex. As a consequence, such factors act as confounders in studies relying solely on self-reported mobile phone use and have to be considered in the analysis. Copyright © 2011 Elsevier Ltd. All rights reserved.
The new pooled cohort equations risk calculator
Preiss, David; Kristensen, Søren L
2015-01-01
disease and any measure of social deprivation. An early criticism of the Pooled Cohort Equations Risk Calculator has been its alleged overestimation of ASCVD risk which, if confirmed in the general population, is likely to result in statin therapy being prescribed to many individuals at lower risk than...
Fisher, Jennifer O; Butte, Nancy F; Mendoza, Patricia M; Wilson, Theresa A; Hodges, Eric A; Reidy, Kathleen C; Deming, Denise
2008-08-01
Twenty-four-hour dietary recalls have been used in large surveys of infant and toddler energy intake, but the accuracy of the method for young children is not well documented. We aimed to determine the accuracy of infant and toddler energy intakes by a single, telephone-administered, multiple-pass 24-h recall as compared with 3-d weighed food records. A within-subjects design was used in which a 24-h recall and 3-d weighed food records were completed within 2 wk by 157 mothers (56 non-Hispanic white, 51 non-Hispanic black, and 50 Hispanic) of 7-11-mo-old infants or 12-24-mo-old toddlers. Child and caregiver anthropometrics, child eating patterns, and caregiver demographics and social desirability were evaluated as correlates of reporting bias. Intakes based on 3-d weighed food records were within 5% of estimated energy requirements. Compared with the 3-d weighed food records, the 24-h recall overestimated energy intake by 13% among infants (740 +/- 154 and 833 +/- 255 kcal, respectively) and by 29% among toddlers (885 +/- 197 and 1140 +/- 299 kcal, respectively). Eating patterns (ie, frequency and location) did not differ appreciably between methods. Macronutrient and micronutrient intakes were higher by 24-h recall than by 3-d weighed food record. Dairy and grains contributed the most energy to the diet and accounted for 74% and 54% of the overestimation seen in infants and toddlers, respectively. Greater overestimation was associated with a greater number of food items reported by the caregiver and lower child weight-for-length z scores. The use of a single, telephone-administered, multiple-pass 24-h recall may significantly overestimate infant or toddler energy and nutrient intakes because of portion size estimation errors.
Overestimation of Knowledge About Word Meanings: The “Misplaced Meaning” Effect
Kominsky, Jonathan F.; Keil, Frank C.
2014-01-01
Children and adults may not realize how much they depend on external sources in understanding word meanings. Four experiments investigated the existence and developmental course of a “Misplaced Meaning” (MM) effect, wherein children and adults overestimate their knowledge about the meanings of various words by underestimating how much they rely on outside sources to determine precise reference. Studies 1 & 2 demonstrate that children and adults show a highly consistent MM effect, and that it ...
Are the performance overestimates given by boys with ADHD self-protective?
Ohan, Jeneva L; Johnston, Charlotte
2002-06-01
Tested the self-protective hypothesis that boys with attention deficit hyperactivity disorder (ADHD) overestimate their performance to protect a positive self-image. We examined the impact of performance feedback on the social and academic performance self-perceptions of 45 boys with and 43 boys without ADHD ages 7 to 12. Consistent with the self-protective hypothesis, positive feedback led to increases in social performance estimates in boys without ADHD but to decreases in estimates given by boys with ADHD. This suggests that boys with ADHD can give more realistic self-appraisals when their self-image has been bolstered. In addition, social performance estimates in boys with ADHD were correlated with measures of self-esteem and positive presentation bias. In contrast, for academic performance estimates, boys in both groups increased their performance estimates after receiving positive versus average or no feedback, and estimates were not correlated with self-esteem or social desirability for boys with ADHD. We conclude that the self-protective hypothesis can account for social performance overestimations given by boys with ADHD but that other factors may better account for their academic performance overestimates.
Kaplan-Meier Survival Analysis Overestimates the Risk of Revision Arthroplasty: A Meta-analysis.
Lacny, Sarah; Wilson, Todd; Clement, Fiona; Roberts, Derek J; Faris, Peter D; Ghali, William A; Marshall, Deborah A
2015-11-01
Although Kaplan-Meier survival analysis is commonly used to estimate the cumulative incidence of revision after joint arthroplasty, it theoretically overestimates the risk of revision in the presence of competing risks (such as death). Because the magnitude of overestimation is not well documented, the potential associated impact on clinical and policy decision-making remains unknown. We performed a meta-analysis to answer the following questions: (1) To what extent does the Kaplan-Meier method overestimate the cumulative incidence of revision after joint replacement compared with alternative competing-risks methods? (2) Is the extent of overestimation influenced by followup time or rate of competing risks? We searched Ovid MEDLINE, EMBASE, BIOSIS Previews, and Web of Science (1946, 1980, 1980, and 1899, respectively, to October 26, 2013) and included article bibliographies for studies comparing estimated cumulative incidence of revision after hip or knee arthroplasty obtained using both Kaplan-Meier and competing-risks methods. We excluded conference abstracts, unpublished studies, or studies using simulated data sets. Two reviewers independently extracted data and evaluated the quality of reporting of the included studies. Among 1160 abstracts identified, six studies were included in our meta-analysis. The principal reason for the steep attrition (1160 to six) was that the initial search was for studies in any clinical area that compared the cumulative incidence estimated using the Kaplan-Meier versus competing-risks methods for any event (not just the cumulative incidence of hip or knee revision); we did this to minimize the likelihood of missing any relevant studies. We calculated risk ratios (RRs) comparing the cumulative incidence estimated using the Kaplan-Meier method with the competing-risks method for each study and used DerSimonian and Laird random effects models to pool these RRs. Heterogeneity was explored using stratified meta-analyses and
Junghaenel, Doerte U; Schneider, Stefan; Broderick, Joan E
2017-09-26
The present study examined whether concordance between patients' and their partners' reports of patient pain severity relates to partners' social support and behavioral responses in couples coping with chronic pain. Fifty-two couples completed questionnaires about the patient's pain severity. Both dyad members also rated the partner's social support and negative, solicitous, and distracting responses toward the patient when in pain. Bivariate correlations showed moderate correspondence between patient and partner ratings of pain severity (r = 0.55) and negative (r = 0.46), solicitous (r = 0.47), and distracting responses (r = 0.53), but lower correspondence for social support (r = 0.28). Twenty-eight couples (54%) were concordant in their perceptions of patient pain; partners overestimated pain in 14 couples (27%), and partners underestimated pain in 10 couples (19%). Couple concordance in pain perceptions was not related to patients' reports; however, it significantly predicted partners' reports: Partners who overestimated pain reported giving more social support (β = 0.383, P = 0.016), fewer negative responses (β = -0.332, P = 0.029), and more solicitous responses (β = 0.438, P = 0.016) than partners who were in agreement or who underestimated pain. Partner overestimation of pain severity is associated with partner-reported but not with patient-reported support-related responses. This finding has important clinical implications for couple interventions in chronic pain. © 2017 American Academy of Pain Medicine. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com
Volume-Dependent Overestimation of Spontaneous Intracerebral Hematoma Volume by the ABC/2 Formula
Chih-Wei Wang; Chun-Jung Juan; Hsian-He Hsu; Hua-Shan Liu; Cheng-Yu Chen; Chun-Jen Hsueh; Hung-Wen Kao; Guo-Shu Huang; Yi-Jui Liu; Chung-Ping Lo
2009-01-01
Background: Although the ABC/2 formula has been widely used to estimate the volume of intracerebral hematoma (ICH), the formula tends to overestimate hematoma volume. The volume-related imprecision of the ABC/2 formula has not been documented quantitatively. Purpose: To investigate the volume-dependent overestimation of the ABC/2 formula by comparing it with computer-assisted volumetric analysis (CAVA). Material and Methods: Forty patients who had suffered spontaneous ICH and who had undergone non-enhanced brain computed tomography scans were enrolled in this study. The ICH volume was estimated based on the ABC/2 formula and also calculated by CAVA. Based on the ICH volume calculated by the CAVA method, the patients were divided into three groups: group 1 consisted of 17 patients with an ICH volume of less than 20 ml; group 2 comprised 13 patients with an ICH volume of 20 to 40 ml; and group 3 was composed of 10 patients with an ICH volume larger than 40 ml. Results: The mean estimated hematoma volume was 43.6 ml when using the ABC/2 formula, compared with 33.8 ml when using the CAVA method. The mean estimated difference was 1.3 ml, 4.4 ml, and 31.4 ml for groups 1, 2, and 3, respectively, corresponding to an estimation error of 9.9%, 16.7%, and 37.1% by the ABC/2 formula (P<0.05). Conclusion: The ABC/2 formula significantly overestimates the volume of ICH. A positive association between the estimation error and the volume of ICH is demonstrated
Voltage and pace-capture mapping of linear ablation lesions overestimates chronic ablation gap size.
O'Neill, Louisa; Harrison, James; Chubb, Henry; Whitaker, John; Mukherjee, Rahul K; Bloch, Lars Ølgaard; Andersen, Niels Peter; Dam, Høgni; Jensen, Henrik K; Niederer, Steven; Wright, Matthew; O'Neill, Mark; Williams, Steven E
2018-04-26
Conducting gaps in lesion sets are a major reason for failure of ablation procedures. Voltage mapping and pace-capture have been proposed for intra-procedural identification of gaps. We aimed to compare gap size measured acutely and chronically post-ablation to macroscopic gap size in a porcine model. Intercaval linear ablation was performed in eight Göttingen minipigs with a deliberate gap of ∼5 mm left in the ablation line. Gap size was measured by interpolating ablation contact force values between ablation tags and thresholding at a low force cut-off of 5 g. Bipolar voltage mapping and pace-capture mapping along the length of the line were performed immediately, and at 2 months, post-ablation. Animals were euthanized and gap sizes were measured macroscopically. Voltage thresholds to define scar were determined by receiver operating characteristic analysis as voltage, pace-capture, and ablation contact force maps. All modalities overestimated chronic gap size, by 1.4 ± 2.0 mm (ablation contact force map), 5.1 ± 3.4 mm (pace-capture), and 9.5 ± 3.8 mm (voltage mapping). Error on ablation contact force map gap measurements were significantly less than for voltage mapping (P = 0.003, Tukey's multiple comparisons test). Chronically, voltage mapping and pace-capture mapping overestimated macroscopic gap size by 11.9 ± 3.7 and 9.8 ± 3.5 mm, respectively. Bipolar voltage and pace-capture mapping overestimate the size of chronic gap formation in linear ablation lesions. The most accurate estimation of chronic gap size was achieved by analysis of catheter-myocardium contact force during ablation.
Overestimation of closed-chamber soil CO2 effluxes at low atmospheric turbulence
Brændholt, Andreas; Larsen, Klaus Steenberg; Ibrom, Andreas
2017-01-01
Soil respiration (R-s) is an important component of ecosystem carbon balance, and accurate quantification of the diurnal and seasonal variation of R-s is crucial for a correct interpretation of the response of R-s to biotic and abiotic factors, as well as for estimating annual soil CO2 efflux rates...... be eliminated if proper mixing of air is ensured, and indeed the use of fans removed the overestimation of R-s rates during low u(*). Artificial turbulent air mixing may thus provide a method to overcome the problems of using closed-chamber gas-exchange measurement techniques during naturally occurring low...
Vossbeck-Elsebusch, Anna N; Waldorf, Manuel; Legenbauer, Tanja; Bauer, Anika; Cordes, Martin; Vocks, Silja
2015-06-01
Body-related avoidance behavior, e.g., not looking in the mirror, is a common feature of eating disorders. It is assumed that it leads to insufficient feedback concerning one's own real body form and might thus contribute to distorted mental representation of one's own body. However, this assumption still lacks empirical foundation. Therefore, the aim of the present study was to examine the relationship between misperception of one's own body and body-related avoidance behavior in N = 78 female patients with Bulimia nervosa and eating disorder not otherwise specified. Body-size misperception was assessed using a digital photo distortion technique based on an individual picture of each participant which was taken in a standardized suit. In a regression analysis with body-related avoidance behavior, body mass index and weight and shape concerns as predictors, only body-related avoidance behavior significantly contributed to the explanation of body-size overestimation. This result supports the theoretical assumption that body-related avoidance behavior makes body-size overestimation more likely.
Debate on the Chernobyl disaster: on the causes of Chernobyl overestimation.
Jargin, Sergei V
2012-01-01
After the Chernobyl accident, many publications appeared that overestimated its medical consequences. Some of them are discussed in this article. Among the motives for the overestimation were anti-nuclear sentiments, widespread among some adherents of the Green movement; however, their attitude has not been wrong: nuclear facilities should have been prevented from spreading to overpopulated countries governed by unstable regimes and regions where conflicts and terrorism cannot be excluded. The Chernobyl accident has hindered worldwide development of atomic industry. Today, there are no alternatives to nuclear power: nonrenewable fossil fuels will become more and more expensive, contributing to affluence in the oil-producing countries and poverty in the rest of the world. Worldwide introduction of nuclear energy will become possible only after a concentration of authority within an efficient international executive. This will enable construction of nuclear power plants in optimally suitable places, considering all sociopolitical, geographic, geologic, and other preconditions. In this way, accidents such as that in Japan in 2011 will be prevented.
Reassessment of soil erosion on the Chinese loess plateau: were rates overestimated?
Zhao, Jianlin; Govers, Gerard
2014-05-01
Several studies have estimated regional soil erosion rates (rill and interrill erosion) on the Chinese loess plateau using an erosion model such as the RUSLE (e.g. Fu et al., 2011; Sun et al., 2013). However, the question may be asked whether such estimates are realistic: studies have shown that the use of models for large areas may lead to significant overestimations (Quinton et al., 2010). In this study, soil erosion rates on the Chinese loess plateau were reevaluated by using field measured soil erosion data from erosion plots (216 plots and 1380 plot years) in combination with a careful extrapolation procedure. Data analysis showed that the relationship between slope and erosion rate on arable land could be well described by erosion-slope relationships reported in the literature (Nearing, 1997). The increase of average erosion rate with slope length was clearly degressive, as could be expected from earlier research. However, for plots with permanent vegetation (grassland, shrub, forest) no relationship was found between erosion rates and slope gradient and/or slope length. This is important, as it implies that spatial variations of erosion on permanently vegetated areas cannot be modeled using topographical functions derived from observations on arable land. Application of relationships developed for arable land will lead to a significant overestimation of soil erosion rates. Based on our analysis we estimate the total soil erosion rate in the Chinese Loess plateau averages ca. 6.78 t ha-1 yr-1 for the whole loess plateau, resulting in a total sediment mobilisation of ca. 0.38 Gt yr-1. Erosion rates on arable land average ca. 15.10 t ha-1 yr-1. These estimates are 2 to 3 times lower than previously published estimates. The main reason why previous estimates are likely to be too high is that the values of (R)USLE parameters such as K, P and LS factor were overestimated. Overestimations of the K factor are due to the reliance of nomograph calculations, resulting
Turner, Benjamin L; Newman, Susan; Reddy, K Ramesh
2006-05-15
Accurate information on the chemical nature of soil phosphorus is essential for understanding its bioavailability and fate in wetland ecosystems. Solution phosphorus-31 nuclear magnetic resonance (31P NMR) spectroscopy was used to assess the conventional colorimetric procedure for phosphorus speciation in alkaline extracts of organic soils from the Florida Everglades. Molybdate colorimetry markedly overestimated organic phosphorus by between 30 and 54% compared to NMR spectroscopy. This was due in large part to the association of inorganic phosphate with organic matter, although the error was exacerbated in some samples by the presence of pyrophosphate, an inorganic polyphosphate that is not detected by colorimetry. The results have important implications for our understanding of phosphorus biogeochemistry in wetlands and suggest that alkaline extraction and solution 31p NMR spectroscopy is the only accurate method for quantifying organic phosphorus in wetland soils.
The Overestimation Phenomenon in a Skill-Based Gaming Context: The Case of March Madness Pools.
Kwak, Dae Hee
2016-03-01
Over 100 million people are estimated to take part in the NCAA Men's Basketball Tournament Championship bracket contests. However, relatively little is known about consumer behavior in skill-based gaming situations (e.g., sports betting). In two studies, we investigated the overestimation phenomenon in the "March Madness" context. In Study 1 (N = 81), we found that individuals who were allowed to make their own predictions were significantly more optimistic about their performance than individuals who did not make their own selections. In Study 2 (N = 197), all subjects participated in a mock competitive bracket pool. In line with the illusion of control theory, results showed that higher self-ratings of probability of winning significantly increased maximum willingness to wager but did not improve actual performance. Lastly, perceptions of high probability of winning significantly contributed to consumers' enjoyment and willingness to participate in a bracket pool in the future.
Overestimation of Knowledge About Word Meanings: The “Misplaced Meaning” Effect
Kominsky, Jonathan F.; Keil, Frank C.
2014-01-01
Children and adults may not realize how much they depend on external sources in understanding word meanings. Four experiments investigated the existence and developmental course of a “Misplaced Meaning” (MM) effect, wherein children and adults overestimate their knowledge about the meanings of various words by underestimating how much they rely on outside sources to determine precise reference. Studies 1 & 2 demonstrate that children and adults show a highly consistent MM effect, and that it is stronger in young children. Study 3 demonstrates that adults are explicitly aware of the availability of outside knowledge, and that this awareness may be related to the strength of the MM effect. Study 4 rules out general overconfidence effects by examining a metalinguistic task in which adults are well-calibrated. PMID:24890038
Sheldon, Kennon M; Gunz, Alexander; Nichols, Charles P; Ferguson, Yuna
2010-02-01
We examined affective forecasting errors as a possible explanation of the perennial appeal of extrinsic values and goals. Study 1 found that although people relatively higher in extrinsic (money, fame, image) compared to intrinsic (growth, intimacy, community) value orientation (REVO) are less happy, they nevertheless believe that attaining extrinsic goals offers a strong potential route to happiness. Study 2's longitudinal experimental design randomly assigned participants to pursue either 3 extrinsic or 3 intrinsic goals over 4 weeks, and REVO again predicted stronger forecasts regarding extrinsic goals. However, not even extrinsically oriented participants gained well-being benefits from attaining extrinsic goals, whereas all participants tended to gain in happiness from attaining intrinsic goals. Study 3 showed that the effect of REVO on forecasts is mediated by extrinsic individuals' belief that extrinsic goals will satisfy autonomy and competence needs. It appears that some people overestimate the emotional benefits of achieving extrinsic goals, to their potential detriment.
Partial report and other sampling procedures overestimate the duration of iconic memory.
Appelman, I B
1980-03-01
In three experiments, subjects estimated the duration of a brief visual image (iconic memory) either directly by adjusting onset of a click to offset of the visual image, or indirectly with a Sperling partial report (sampling) procedure. The results indicated that partial report and other sampling procedures may reflect other brief phenomena along with iconic memory. First, the partial report procedure yields a greater estimate of the duration of iconic memory than the more direct click method. Second, the partial report estimate of the duration of iconic memory is affected if the subject is required to simultaneously retain a list of distractor items (memory load), while the click method estimate of the duration of iconic memory is not affected by a memory load. Finally, another sampling procedure based on visual cuing yields different estimates of the duration of iconic memory depending on how many items are cued. It was concluded that partial report and other sampling procedures overestimate the duration of iconic memory.
Overestimation of test performance by ROC analysis: Effect of small sample size
Seeley, G.W.; Borgstrom, M.C.; Patton, D.D.; Myers, K.J.; Barrett, H.H.
1984-01-01
New imaging systems are often observer-rated by ROC techniques. For practical reasons the number of different images, or sample size (SS), is kept small. Any systematic bias due to small SS would bias system evaluation. The authors set about to determine whether the area under the ROC curve (AUC) would be systematically biased by small SS. Monte Carlo techniques were used to simulate observer performance in distinguishing signal (SN) from noise (N) on a 6-point scale; P(SN) = P(N) = .5. Four sample sizes (15, 25, 50 and 100 each of SN and N), three ROC slopes (0.8, 1.0 and 1.25), and three intercepts (0.8, 1.0 and 1.25) were considered. In each of the 36 combinations of SS, slope and intercept, 2000 runs were simulated. Results showed a systematic bias: the observed AUC exceeded the expected AUC in every one of the 36 combinations for all sample sizes, with the smallest sample sizes having the largest bias. This suggests that evaluations of imaging systems using ROC curves based on small sample size systematically overestimate system performance. The effect is consistent but subtle (maximum 10% of AUC standard deviation), and is probably masked by the s.d. in most practical settings. Although there is a statistically significant effect (F = 33.34, P<0.0001) due to sample size, none was found for either the ROC curve slope or intercept. Overestimation of test performance by small SS seems to be an inherent characteristic of the ROC technique that has not previously been described
Energy costs of surgery as measured by the doubly labeled water (2H218O) method
Novick, W.M.; Nusbaum, M.; Stein, T.P.
1988-01-01
Energy expenditure before and after surgery was determined in seven patients by the doubly labeled water ( 2 H 2 18 O) method (DLW). The values were compared with values obtained by respiratory gas exchange by means of a metabolic measuring cart (MMC). Patients were maintained on total parenteral nutrition before and after trauma. The principal finding was an increase in the rate of CO 2 production of 11.9 +/- 5.0% after surgery. This corresponds to a 267 +/- increase in energy expenditure (p less than 0.05). No trauma-associated change in energy expenditure was found with the MMC. The correlation of preoperative values from MMC and DLW was not statistically significant (r = 0.25), nor was the correlation of MMC and the Harris-Benedict equation, but the correlation of DLW with Harris-Benedict equation was statistically significant (r = 0.73, p less than 0.05). We suggest that the discrepancy is because the DLW method measures the cumulative energy expenditure over a period, whereas the MMC gives a spot measurement
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Waldinger, Marcel D; Zwinderman, Aeilko H; Olivier, Berend; Schweitzer, Dave H
2008-02-01
The intravaginal ejaculation latency time (IELT) behaves in a skewed manner and needs the appropriate statistics for correct interpretation of treatment results. To explain the rightful use of geometrical mean IELT values and the fold increase of the geometric mean IELT because of the positively skewed IELT distribution. Linking theoretical arguments to the outcome of several selective serotonin reuptake inhibitor and modern antidepressant study results. Geometric mean IELT and fold increase of geometrical mean IELT. Log-transforming each separate IELT measurement of each individual man is the basis for the calculation of the geometric mean IELT. A drug-induced positively skewed IELT distribution necessitates the calculation of the geometric mean IELTs at baseline and during drug treatment. In a positively skewed IELT distribution, the use of the "arithmetic" mean IELT risks an overestimation of the drug-induced ejaculation delay as the mean IELT is always higher than the geometric mean IELT. Strong ejaculation-delaying drugs give rise to a strong positively skewed IELT distribution, whereas weak ejaculation-delaying drugs give rise to (much) less skewed IELT distributions. Ejaculation delay is expressed in fold increase of the geometric mean IELT. Drug-induced ejaculatory performance discloses a positively skewed IELT distribution, requiring the use of the geometric mean IELT and the fold increase of the geometric mean IELT.
Plant pathogens as biocontrol agents of Cirsium arvense – an overestimated approach?
Esther Müller
2011-11-01
Full Text Available Cirsium arvense is one of the worst weeds in agriculture. As herbicides are not very effective and not accepted by organic farming and special habitats, possible biocontrol agents have been investigated since many decades. In particular plant pathogens of C. arvense have received considerable interest and have been promoted as “mycoherbicides” or “bioherbicides”. A total of 10 fungi and one bacterium have been proposed and tested as biocontrol agents against C. arvense. A variety of experiments analysed the noxious influence of spores or other parts of living fungi or bacteria on plants while others used fungal or bacterial products, usually toxins. Also combinations of spores with herbicides and combinations of several pathogens were tested. All approaches turned out to be inappropriate with regard to target plant specificity, effectiveness and application possibilities. As yet, none of the tested species or substances has achieved marketability, despite two patents on the use of Septoria cirsii and Phomopsis cirsii. We conclude that the potential of pathogens for biocontrol of C. arvense has largely been overestimated.
Mobility overestimation due to gated contacts in organic field-effect transistors
Bittle, Emily G.; Basham, James I.; Jackson, Thomas N.; Jurchescu, Oana D.; Gundlach, David J.
2016-01-01
Parameters used to describe the electrical properties of organic field-effect transistors, such as mobility and threshold voltage, are commonly extracted from measured current–voltage characteristics and interpreted by using the classical metal oxide–semiconductor field-effect transistor model. However, in recent reports of devices with ultra-high mobility (>40 cm2 V−1 s−1), the device characteristics deviate from this idealized model and show an abrupt turn-on in the drain current when measured as a function of gate voltage. In order to investigate this phenomenon, here we report on single crystal rubrene transistors intentionally fabricated to exhibit an abrupt turn-on. We disentangle the channel properties from the contact resistance by using impedance spectroscopy and show that the current in such devices is governed by a gate bias dependence of the contact resistance. As a result, extracted mobility values from d.c. current–voltage characterization are overestimated by one order of magnitude or more. PMID:26961271
Kim, Miso; Lee, Hongmie
2010-12-01
The study aimed to analyze the lifestyles, weight control behavior, dietary habits, and depression of female university students. The subjects were 532 students from 8 universities located in 4 provinces in Korea. According to percent ideal body weight, 33 (6.4%), 181 (34.0%), 283 (53.2%), 22 (4.1%) and 13 (2.5%) were severely underweight, underweight, normal, overweight and obese, respectively, based on self-reported height and weight. As much as 64.1% and only 2.4%, respectively, overestimated and underestimated their body weight status. Six overweight subjects were excluded from overestimation group for the purpose of this study, resulting in overestimation group consisting of only underweight and normal weight subjects. Compared to those from the normal perception group, significantly more subjects from the overestimation group were currently smoking (P = 0.017) and drank more often than once a week (P = 0.015), without any significant differences in dietary habits. Despite similar BMIs, subjects who overestimated their own weight statuses had significantly higher weight dissatisfaction (P = 0.000), obesity stress (P = 0.000), obsession to lose weight (P = 0.007) and depression (P = 0.018). Also, more of them wanted to lose weight (P = 0.000), checked their body weights more often than once a week (P = 0.025) and had dieting experiences using 'reducing meal size' (P = 0.012), 'reducing snacks' (P = 0.042) and 'taking prescribed pills' (P = 0.032), and presented 'for a wider range of clothes selection' as the reason for weight loss (P = 0.039), although none was actually overweight or obese. Unlike the case with overestimating one's own weight, being overweight was associated with less drinking (P = 0.035) and exercising more often (P = 0.001) and for longer (P = 0.001) and healthier reasons for weight control (P = 0.002), despite no differences in frequency of weighing and depression. The results showed that weight overestimation, independent of weight status
S. Q. Zhao
2009-08-01
Full Text Available Land use change is critical in determining the distribution, magnitude and mechanisms of terrestrial carbon budgets at the local to global scales. To date, almost all regional to global carbon cycle studies are driven by a static land use map or land use change statistics with decadal time intervals. The biases in quantifying carbon exchange between the terrestrial ecosystems and the atmosphere caused by using such land use change information have not been investigated. Here, we used the General Ensemble biogeochemical Modeling System (GEMS, along with consistent and spatially explicit land use change scenarios with different intervals (1 yr, 5 yrs, 10 yrs and static, respectively, to evaluate the impacts of land use change data frequency on estimating regional carbon sequestration in the southeastern United States. Our results indicate that ignoring the detailed fast-changing dynamics of land use can lead to a significant overestimation of carbon uptake by the terrestrial ecosystem. Regional carbon sequestration increased from 0.27 to 0.69, 0.80 and 0.97 Mg C ha^{−1} yr^{−1} when land use change data frequency shifting from 1 year to 5 years, 10 years interval and static land use information, respectively. Carbon removal by forest harvesting and prolonged cumulative impacts of historical land use change on carbon cycle accounted for the differences in carbon sequestration between static and dynamic land use change scenarios. The results suggest that it is critical to incorporate the detailed dynamics of land use change into local to global carbon cycle studies. Otherwise, it is impossible to accurately quantify the geographic distributions, magnitudes, and mechanisms of terrestrial carbon sequestration at the local to global scales.
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Overestimation of reliability by Guttman’s λ4, λ5, and λ6, and the greatest lower bound
Oosterwijk, P.R.; van der Ark, L.A.; Sijtsma, K.; van der Ark, L.A.; Wiberg, M.; Culpepper, S.A.; Douglas, J.A.; Wang, W.-C.
2017-01-01
For methods using statistical optimization to estimate lower bounds to test-score reliability, we investigated the degree to which they overestimate true reliability. Optimization methods do not only exploit real relationships between items but also tend to capitalize on sampling error and do this
Kim, Bohyun; Kim, Kyoung Won; Kim, So Yeon; Park, So Hyun; Lee, Jeongjin; Song, Gi Won; Jung, Dong-Hwan; Ha, Tae-Yong; Lee, Sung Gyu
2017-01-01
To compare the length of the right hepatic duct (RHD) measured on rotatory coronal 2D MR cholangiography (MRC), rotatory axial 2D MRC, and reconstructed 3D MRC. Sixty-seven donors underwent coronal and axial 2D projection MRC and 3D MRC. RHD length was measured and categorized as ultrashort (≤1 mm), short (>1-14 mm), and long (>14 mm). The measured length, frequency of overestimation, and the degree of underestimation between two 2D MRC sets were compared to 3D MRC. The length of the RHD from 3D MRC, coronal 2D MRC, and axial 2D MRC showed significant difference (p < 0.05). RHD was frequently overestimated on the coronal than on axial 2D MRC (61.2 % vs. 9 %; p <.0001). On coronal 2D MRC, four (6 %) with short RHD and one (1.5 %) with ultrashort RHD were over-categorized as long RHD. On axial 2D MRC, overestimation was mostly <1 mm (83.3 %), none exceeding 3 mm or over-categorized. The degree of underestimation between the two projection planes was comparable. Coronal 2D MRC overestimates the RHD in liver donors. We suggest adding axial 2D MRC to conventional coronal 2D MRC in the preoperative workup protocol for living liver donors to avoid unexpected confrontation with multiple ductal openings when harvesting the graft. (orig.)
Kim, Bohyun [University of Ulsan College of Medicine, Department of Radiology, Asan Medical Center, 88, Olympic-ro 43-gil, Songpa-gu, Seoul (Korea, Republic of); Ajou University School of Medicine, Department of Radiology, Ajou University Medical Center, Suwon (Korea, Republic of); Kim, Kyoung Won; Kim, So Yeon; Park, So Hyun [University of Ulsan College of Medicine, Department of Radiology, Asan Medical Center, 88, Olympic-ro 43-gil, Songpa-gu, Seoul (Korea, Republic of); Lee, Jeongjin [Soongsil University, School of Computer Science and Engineering, Seoul (Korea, Republic of); Song, Gi Won; Jung, Dong-Hwan; Ha, Tae-Yong; Lee, Sung Gyu [University of Ulsan College of Medicine, Department of Surgery, Division of Hepatobiliary and Liver Transplantation Surgery, Asan Medical Center, Seoul (Korea, Republic of)
2017-05-15
To compare the length of the right hepatic duct (RHD) measured on rotatory coronal 2D MR cholangiography (MRC), rotatory axial 2D MRC, and reconstructed 3D MRC. Sixty-seven donors underwent coronal and axial 2D projection MRC and 3D MRC. RHD length was measured and categorized as ultrashort (≤1 mm), short (>1-14 mm), and long (>14 mm). The measured length, frequency of overestimation, and the degree of underestimation between two 2D MRC sets were compared to 3D MRC. The length of the RHD from 3D MRC, coronal 2D MRC, and axial 2D MRC showed significant difference (p < 0.05). RHD was frequently overestimated on the coronal than on axial 2D MRC (61.2 % vs. 9 %; p <.0001). On coronal 2D MRC, four (6 %) with short RHD and one (1.5 %) with ultrashort RHD were over-categorized as long RHD. On axial 2D MRC, overestimation was mostly <1 mm (83.3 %), none exceeding 3 mm or over-categorized. The degree of underestimation between the two projection planes was comparable. Coronal 2D MRC overestimates the RHD in liver donors. We suggest adding axial 2D MRC to conventional coronal 2D MRC in the preoperative workup protocol for living liver donors to avoid unexpected confrontation with multiple ductal openings when harvesting the graft. (orig.)
Craen, S. de Twisk, D.A.M. Hagenzieker, M.P. Elffers, H. & Brookhuis, K.A.
2011-01-01
In this study the authors argue that drivers have to make an assessment of their own driving skills, in order to sufficiently adapt to their task demands in traffic. There are indications that drivers in general, but novice drivers in particular, overestimate their driving skills. However, study
Catarina Bertaso Andreatta Gottschall
2004-12-01
.BACKGROUND: Malnutrition is frequent in cirrhotic patients, and its assessment is difficult. Functional assessment through a dynamometer is a simple method and could minimize these drawbacks. Harris-Benedict prediction formulae estimates the resting energy expenditure but has not been validated for this population. One alternative is the use of indirect calorimetry. AIM: To assess nutritional status in cirrhotic patients and estimates the resting energy expenditure through indirect calorimetry and compares it to Harris-Benedict. PATIENTS AND METHODS: Thirty four adult hepatitis C cirrhotic outpatients were studied, classified by Child-Pugh and model of end-stage liver disease score. The resting energy expenditure was predicted through Harris-Benedict and measured by indirect calorimetry. Nutritional assessment was done through anthropometry, subjective global assessment, hand-grip strength and a 3-day recall. RESULTS: Fifteen (44.2% were Child-Pug A, 12 (35.3% B and 7 (20.6% C, and 33 (97.1% had model of end-stage liver disease scores less than 20. The resting energy expenditure predicted was higher than the measured (Harris-Benedict 1404.5 ± 150.3 kcal; indirect calorimetry 1059.9 ± 309.6 kcal. The prevalence of malnutrition varied between methods (body mass index, muscle arm circumference, subjective global assessment, triceps skinfold thickness and hand-grip strength: 0; 5.9; 17.6; 35.3 and 79.4%, accordingly. Calories and proteins intake were 80% and 85% of recommended amounts and there was inadequate intake of calcium, magnesium, iron and zinc. CONCLUSION: Malnutrition was frequent and hand-grip strength seemed to be the most sensitive method for its diagnosis. Calories and protein intakes were inadequate. Considering that the predicted resting energy expenditure was higher than the measured one and the need to offer higher caloric intake, the use of the predicting equation may replace indirect calorimetry.
Why overestimate or underestimate chronic kidney disease when correct estimation is possible?
De Broe, Marc E; Gharbi, Mohamed Benghanem; Zamd, Mohamed; Elseviers, Monique
2017-04-01
There is no doubt that the introduction of the Kidney Disease: Improving Global Outcomes (KDIGO) guidelines 14 years ago, and their subsequent updates, have substantially contributed to the early detection of different stages of chronic kidney disease (CKD). Several recent studies from different parts of the world mention a CKD prevalence of 8-13%. However, some editorials and reviews have begun to describe the weaknesses of a substantial number of studies. Maremar (maladies rénales chroniques au Maroc) is a recently published prevalence study of CKD, hypertension, diabetes and obesity in a randomized, representative and high response rate (85%) sample of the adult population of Morocco that strictly applied the KDIGO guidelines. When adjusted to the actual adult population of Morocco (2015), a rather low prevalence of CKD (2.9%) was found. Several reasons for this low prevalence were identified; the tagine-like population pyramid of the Maremar population was a factor, but even more important were the confirmation of proteinuria found at first screening and the proof of chronicity of decreased estimated glomerular filtration rate (eGFR), eliminating false positive results. In addition, it was found that when an arbitrary single threshold of eGFR (55 years of age), particularly in those without proteinuria, haematuria or hypertension. It also resulted in a significant 'underdiagnosis' (false negatives) in younger individuals with an eGFR >60 mL/min/1.73 m2 and below the third percentile of their age-/gender-category. The use of the third percentile eGFR level as a cut-off, based on age-gender-specific reference values of eGFR, allows the detection of these false positives and negatives. There is an urgent need for additional quality studies of the prevalence of CKD using the recent KDIGO guidelines in the correct way, to avoid overestimation of the true disease state of CKD by ≥50% with potentially dramatic consequences. © The Author 2017. Published by Oxford
Limb Symmetry Indexes Can Overestimate Knee Function After Anterior Cruciate Ligament Injury.
Wellsandt, Elizabeth; Failla, Mathew J; Snyder-Mackler, Lynn
2017-05-01
Study Design Prospective cohort. Background The high risk of second anterior cruciate ligament (ACL) injuries after return to sport highlights the importance of return-to-sport decision making. Objective return-to-sport criteria frequently use limb symmetry indexes (LSIs) to quantify quadriceps strength and hop scores. Whether using the uninvolved limb in LSIs is optimal is unknown. Objectives To evaluate the uninvolved limb as a reference standard for LSIs utilized in return-to-sport testing and its relationship with second ACL injury rates. Methods Seventy athletes completed quadriceps strength and 4 single-leg hop tests before anterior cruciate ligament reconstruction (ACLR) and 6 months after ACLR. Limb symmetry indexes for each test compared involved-limb measures at 6 months to uninvolved-limb measures at 6 months. Estimated preinjury capacity (EPIC) levels for each test compared involved-limb measures at 6 months to uninvolved-limb measures before ACLR. Second ACL injuries were tracked for a minimum follow-up of 2 years after ACLR. Results Forty (57.1%) patients achieved 90% LSIs for quadriceps strength and all hop tests. Only 20 (28.6%) patients met 90% EPIC levels (comparing the involved limb at 6 months after ACLR to the uninvolved limb before ACLR) for quadriceps strength and all hop tests. Twenty-four (34.3%) patients who achieved 90% LSIs for all measures 6 months after ACLR did not achieve 90% EPIC levels for all measures. Estimated preinjury capacity levels were more sensitive than LSIs in predicting second ACL injuries (LSIs, 0.273; 95% confidence interval [CI]: 0.010, 0.566 and EPIC, 0.818; 95% CI: 0.523, 0.949). Conclusion Limb symmetry indexes frequently overestimate knee function after ACLR and may be related to second ACL injury risk. These findings raise concern about whether the variable ACL return-to-sport criteria utilized in current clinical practice are stringent enough to achieve safe and successful return to sport. Level of Evidence
Overestimation of Crop Root Biomass in Field Experiments Due to Extraneous Organic Matter.
Hirte, Juliane; Leifeld, Jens; Abiven, Samuel; Oberholzer, Hans-Rudolf; Hammelehle, Andreas; Mayer, Jochen
2017-01-01
Root biomass is one of the most relevant root parameters for studies of plant response to environmental change, soil carbon modeling or estimations of soil carbon sequestration. A major source of error in root biomass quantification of agricultural crops in the field is the presence of extraneous organic matter in soil: dead roots from previous crops, weed roots, incorporated above ground plant residues and organic soil amendments, or remnants of soil fauna. Using the isotopic difference between recent maize root biomass and predominantly C3-derived extraneous organic matter, we determined the proportions of maize root biomass carbon of total carbon in root samples from the Swiss long-term field trial "DOK." We additionally evaluated the effects of agricultural management (bio-organic and conventional), sampling depth (0-0.25, 0.25-0.5, 0.5-0.75 m) and position (within and between maize rows), and root size class (coarse and fine roots) as defined by sieve mesh size (2 and 0.5 mm) on those proportions, and quantified the success rate of manual exclusion of extraneous organic matter from root samples. Only 60% of the root mass that we retrieved from field soil cores was actual maize root biomass from the current season. While the proportions of maize root biomass carbon were not affected by agricultural management, they increased consistently with soil depth, were higher within than between maize rows, and were higher in coarse (>2 mm) than in fine (≤2 and >0.5) root samples. The success rate of manual exclusion of extraneous organic matter from root samples was related to agricultural management and, at best, about 60%. We assume that the composition of extraneous organic matter is strongly influenced by agricultural management and soil depth and governs the effect size of the investigated factors. Extraneous organic matter may result in severe overestimation of recovered root biomass and has, therefore, large implications for soil carbon modeling and estimations
Standard duplex criteria overestimate the degree of stenosis after eversion carotid endarterectomy.
Benzing, Travis; Wilhoit, Cameron; Wright, Sharee; McCann, P Aaron; Lessner, Susan; Brothers, Thomas E
2015-06-01
, 146-432 cm/s) after eCEA that were subsequently examined by axial imaging, the mean percentage stenosis was 8% ± 11% by NASCET, 11% ± 5% by ECST, and 20% ± 9% by CSA criteria. For eight pCEA arteries with PSV >125 cm/s (median velocity, 148 cm/s; interquartile range, 139-242 cm/s), the corresponding NASCET, ECST, and CSA stenoses were 8% ± 35%, 26% ± 32%, and 25% ± 33%, respectively. NASCET internal carotid diameter reduction of at least 50% was noted by axial imaging after two of the eight pCEAs, and the PSV exceeded 200 cm/s in each case. The presence of hemodynamically significant carotid artery restenosis may be overestimated by standard duplex criteria after eCEA and perhaps after pCEA. Insufficient information currently exists to determine what PSV does correspond to hemodynamically significant restenosis. Published by Elsevier Inc.
regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.
Gross, F.
1986-01-01
Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs
Zhang Lei; Wang Shuxiao; Wu Qingru; Meng Yang; Yang Hai; Wang Fengyang; Hao Jiming
2012-01-01
Non-ferrous metal smelting takes up a large proportion of the anthropogenic mercury emission inventory in China. Zinc, lead and copper smelting are three leading sources. Onsite measurements of mercury emissions were conducted for six smelters. The mercury emission factors were 0.09–2.98 g Hg/t metal produced. Acid plants with the double-conversion double-absorption process had mercury removal efficiency of over 99%. In the flue gas after acid plants, 45–88% was oxidized mercury which can be easily scavenged in the flue gas scrubber. 70–97% of the mercury was removed from the flue gas to the waste water and 1–17% to the sulfuric acid product. Totally 0.3–13.5% of the mercury in the metal concentrate was emitted to the atmosphere. Therefore, acid plants in non-ferrous metal smelters have significant co-benefit on mercury removal, and the mercury emission factors from Chinese non-ferrous metal smelters were probably overestimated in previous studies. - Highlights: ► Acid plants in smelters provide significant co-benefits for mercury removal (over 99%). ► Most of the mercury in metal concentrates for smelting ended up in waste water. ► Previously published emission factors for Chinese metal smelters were probably overestimated. - Acid plants in smelters have high mercury removal efficiency, and thus mercury emission factors for Chinese non-ferrous metal smelters were probably overestimated.
Skallerup, Anders; Nygaard, Louis; Olesen, Søren Schou; Vinter-Jensen, Lars; Køhler, Marianne; Rasmussen, Henrik Højgaard
2017-09-01
Intestinal failure (IF) is a serious and common complication of short bowel syndrome with patients depending on parenteral nutrition (PN) support. Effective nutrition management requires an accurate estimation of the patient's basal metabolic rate (BMR) to avoid underfeeding or overfeeding. However, indirect calorimetry, considered the gold standard for BMR assessment, is a time- and resource-consuming procedure. Consequently, several equations for prediction of BMR have been developed in different settings, but their accuracy in patients with IF are yet to be investigated. We evaluated the accuracy of predicted BMR in clinically stable patients with IF dependent on home parenteral nutrition (HPN). In total, 103 patients with IF were included. We used indirect calorimetry for assessment of BMR and calculated predicted BMR using different equations based on anthropometric and/or bioelectrical impedance parameters. The accuracy of predicted BMR was evaluated using Bland-Altman analysis with measured BMR as the gold standard. The average measured BMR was 1272 ± 245 kcal/d. The most accurate estimations of BMR were obtained using the Harris-Benedict equation (mean bias, 14 kcal/d [ P = .28]; limits of agreement [LoA], -238 to 266 kcal/d) and the Johnstone equation (mean bias, -16 kcal/d [ P = .24]; LoA, -285 to 253 kcal/d). For both equations, 67% of patients had a predicted BMR from 90%-110% All other equations demonstrated a statistically and clinically significant difference between measured and predicted BMR. The Harris-Benedict and Johnstone equations reliably predict BMR in two-thirds of clinically stable patients with IF on HPN.
Differential Equations Compatible with KZ Equations
Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.
2000-01-01
We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions
Ching, Terence H W; Williams, Monnica T; Siev, Jedidiah; Olatunji, Bunmi O
2018-05-01
Disgust has been shown to perform a "disease-avoidance" function in contamination fears. However, no studies have examined the relevance of disgust to obsessive-compulsive (OC) concerns about sexual orientation (e.g., fear of one's sexual orientation transforming against one's will, and compulsive avoidance of same-sex and/or gay or lesbian individuals to prevent that from happening). Therefore, we investigated whether the specific domain of contamination-based disgust (i.e., evoked by the perceived threat of transmission of essences between individuals) predicted OC concerns about sexual orientation, and whether this effect was moderated/amplified by obsessive beliefs, in evaluation of a "sexual orientation transformation-avoidance" function. We recruited 283 self-identified heterosexual college students (152 females, 131 males; mean age = 20.88 years, SD = 3.19) who completed three measures assessing disgust, obsessive beliefs, and OC concerns about sexual orientation. Results showed that contamination-based disgust (β = .17), responsibility/threat overestimation beliefs (β = .15), and their interaction (β = .17) each uniquely predicted OC concerns about sexual orientation, ts = 2.22, 2.50, and 2.90, ps contamination-based disgust accompanied by strong responsibility/threat overestimation beliefs predicted more severe OC concerns about sexual orientation, β = .48, t = 3.24, p contamination-based disgust, and exacerbated by responsibility/threat overestimation beliefs. Treatment for OC concerns about sexual orientation should target such beliefs.
Thorlund, Kristian; Imberger, Georgina; Walsh, Michael
2011-01-01
Meta-analyses including a limited number of patients and events are prone to yield overestimated intervention effect estimates. While many assume bias is the cause of overestimation, theoretical considerations suggest that random error may be an equal or more frequent cause. The independent impact...... of random error on meta-analyzed intervention effects has not previously been explored. It has been suggested that surpassing the optimal information size (i.e., the required meta-analysis sample size) provides sufficient protection against overestimation due to random error, but this claim has not yet been...
Shore, B.W.
1981-01-01
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence
Johnston, B J; Blinston, G E; Jugdutt, B I
1994-01-01
To assess the effect of early regional diastolic shape distortion or bulging of infarct zones due to infarct expansion on estimates of regional left ventricular dysfunction and infarct size by two-dimensional echocardiographic imaging. Quantitative two-dimensional echocardiograms from patients with a first Q wave myocardial infarction and creatine kinase infarct size data, and normal subjects, were subjected to detailed analysis of regional left ventricular dysfunction and shape distortion in short-axis images by established methods. Regional left ventricular asynergy (akinesis and dyskinesis) and shape distortion indices (eg, peak [Pk]/radius [ri]) were measured on endocardial diastolic outlines of short-axis images in 43 postinfarction patients (28 anterior and 15 inferior, 5.9 h after onset) and 11 normal subjects (controls). In the infarction group, endocardial surface area of asynergy was calculated by three-dimensional reconstruction of the images and infarct size from serial creatine kinase blood levels. Diastolic bulging of asynergic zones was found in all infarction patients. The regional shape distortion indices characterizing the area between the 'actual' bulging asynergic segment and the derived 'ideal' circular segment (excluding the bulge) on indexed sections were greater in infarct than control groups (Pk/ri 0.31 versus 0, P 0.001). Importantly, the degree of distortion correlated with overestimation of asynergy (r = 0.89, P < 0.001), and the relation between infarct size and total 'ideal' asynergy showed a leftward shift from that with 'actual' asynergy. Early regional diastolic bulging of the infarct zone results in overestimation of regional ventricular dysfunction, especially in patients with anterior infarction. This effect should be considered when assessing effects of therapy on infarct size, remodelling and dysfunction using tomographical imaging.
Luyat, Marion; Domino, Delphine; Noël, Myriam
2008-12-01
Falls are frequent in the elderly and account for medical complications and loss of autonomy. Affordance, a concept proposed by Gibson, can help to understand a possible cause of falls. An affordance is defined as a potentiality of action offered by the environment in relation with both the properties of this environment and the properties of the organism. Most of our daily activities reflect a perfect adjustment between the perception of these potentialities of action and our actual action abilities. In other words, we correctly perceive affordances. However, in the elderly, postural abilities are reduced and equilibration is more unstable. Thus, some falls could result from a misperception of the affordances of posturability. The aim of our study was to test the hypothesis that cognitive overestimation of real postural abilities in the elderly may cause falls. There would be a gap between what the old subjects believe to be able to do and what they actually can do. Fifteen young adults (mean age = 24 years) and fifteen older adults (mean age = 72 years) had to judge if they were able to stand upright on an inclined surface. The exploration of the inclined surface was made in two conditions: visually and also by haptics (without vision with a cane). In a second part, we measured their real postural stance on the inclined surface. The results show that the perceptual judgments were not different among old and young people. However, as expected, the old subjects had lower postural boundaries than the younger. They could stand on lower inclinations of the surface. These results show an involution of the perception of the affordances in aging. They support the hypothesis of a cognitive overestimation of action abilities in the elderly, possibly due to a difficulty to actualize the new limits for action.
Baskerville, Jerry Ray; Herrick, John
2012-02-01
This study focuses on clinically assigned prospective estimated pretest probability and pretest perception of legal risk as independent variables in the ordering of multidetector computed tomographic (MDCT) head scans. Our primary aim is to measure the association between pretest probability of a significant finding and pretest perception of legal risk. Secondarily, we measure the percentage of MDCT scans that physicians would not order if there was no legal risk. This study is a prospective, cross-sectional, descriptive analysis of patients 18 years and older for whom emergency medicine physicians ordered a head MDCT. We collected a sample of 138 patients subjected to head MDCT scans. The prevalence of a significant finding in our population was 6%, yet the pretest probability expectation of a significant finding was 33%. The legal risk presumed was even more dramatic at 54%. These data support the hypothesis that physicians presume the legal risk to be significantly higher than the risk of a significant finding. A total of 21% or 15% patients (95% confidence interval, ±5.9%) would not have been subjected to MDCT if there was no legal risk. Physicians overestimated the probability that the computed tomographic scan would yield a significant result and indicated an even greater perceived medicolegal risk if the scan was not obtained. Physician test-ordering behavior is complex, and our study queries pertinent aspects of MDCT testing. The magnification of legal risk vs the pretest probability of a significant finding is demonstrated. Physicians significantly overestimated pretest probability of a significant finding on head MDCT scans and presumed legal risk. Copyright © 2012 Elsevier Inc. All rights reserved.
Scheduling Diet for Diabetes Mellitus Patients using Genetic Algorithm
Syahputra, M. F.; Felicia, V.; Rahmat, R. F.; Budiarto, R.
2017-01-01
Diabetes Melitus (DM) is one of metabolic diseases which affects on productivity and lowers the human resources quality. This disease can be controlled by maintaining and regulating balanced and healthy lifestyle especially for daily diet. However, nowadays, there is no system able to help DM patient to get any information of proper diet. Therefore, an approach is required to provide scheduling diet every day in a week with appropriate nutrition for DM patients to help them regulate their daily diet for healing this disease. In this research, we calculate the number of caloric needs using Harris-Benedict equation and propose genetic algorithm for scheduling diet for DM patient. The results show that the greater the number of individuals, the greater the more the possibility of changes in fitness score approaches the best fitness score. Moreover, the greater the created generation, the more the opportunites to obtain best individual with fitness score approaching 0 or equal to 0.
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
Equating error in observed-score equating
van der Linden, Willem J.
2006-01-01
Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of
Andrea Schaller
2016-01-01
Full Text Available Introduction. The aim of the present study was to determine the closeness of agreement between a self-reported and an objective measure of physical activity in low back pain patients and healthy controls. Beyond, influencing factors on overestimation were identified. Methods. 27 low back pain patients and 53 healthy controls wore an accelerometer (objective measure for seven consecutive days and answered a questionnaire on physical activity (self-report over the same period of time. Differences between self-reported and objective data were tested by Wilcoxon test. Bland-Altman analysis was conducted for describing the closeness of agreement. Linear regression models were calculated to identify the influence of age, sex, and body mass index on the overestimation by self-report. Results. Participants overestimated self-reported moderate activity in average by 42 min/day (p=0.003 and vigorous activity by 39 min/day (p<0.001. Self-reported sedentary time was underestimated by 122 min/day (p<0.001. No individual-related variables influenced the overestimation of physical activity. Low back pain patients were more likely to underestimate sedentary time compared to healthy controls. Discussion. In rehabilitation and health promotion, the application-oriented measurement of physical activity remains a challenge. The present results contradict other studies that had identified an influence of age, sex, and body mass index on the overestimation of physical activity.
Zhou, Cheng; Penner, Joyce E.
2017-01-01
Observation-based studies have shown that the aerosol cloud lifetime effect or the increase of cloud liquid water path (LWP) with increased aerosol loading may have been overestimated in climate models. Here, we simulate shallow warm clouds on 27 May 2011 at the southern Great Plains (SGP) measurement site established by the Department of Energy's (DOE) Atmospheric Radiation Measurement (ARM) program using a single-column version of a global climate model (Community Atmosphere Model or CAM) and a cloud resolving model (CRM). The LWP simulated by CAM increases substantially with aerosol loading while that in the CRM does not. The increase of LWP in CAM is caused by a large decrease of the autoconversion rate when cloud droplet number increases. In the CRM, the autoconversion rate is also reduced, but this is offset or even outweighed by the increased evaporation of cloud droplets near the cloud top, resulting in an overall decrease in LWP. Our results suggest that climate models need to include the dependence of cloud top growth and the evaporation/condensation process on cloud droplet number concentrations.
van Haarst, Ernst P; Bosch, J L H Ruud
2012-09-01
We sought criteria for nocturnal polyuria in asymptomatic, nonurological adults of all ages by reporting reference values of the ratio of daytime and nighttime urine volumes, and finding nocturia predictors. Data from a database of frequency-volume charts from a reference population of 894 nonurological, asymptomatic volunteers of all age groups were analyzed. The nocturnal polyuria index and the nocturia index were calculated and factors influencing these values were determined by multivariate analysis. The nocturnal polyuria index had wide variation but a normal distribution with a mean ± SD of 30% ± 12%. The 95th percentile of the values was 53%. Above this cutoff a patient had nocturnal polyuria. This value contrasts with the International Continence Society definition of 33% but agrees with several other reports. On multivariate regression analysis with the nocturnal polyuria index as the dependent variable sleeping time, maximum voided volume and age were the covariates. However, the increase in the nocturnal polyuria index by age was small. Excluding polyuria and nocturia from analysis did not alter the results in a relevant way. The nocturnal voiding frequency depended on sleeping time and maximum voided volume but most of all on the nocturia index. The prevalence of nocturnal polyuria is overestimated. We suggest a new cutoff value for the nocturnal polyuria index, that is nocturnal polyuria exists when the nocturnal polyuria index exceeds 53%. The nocturia index is the best predictor of nocturia. Copyright © 2012 American Urological Association Education and Research, Inc. Published by Elsevier Inc. All rights reserved.
Garcia Moreira, Vanessa; Beridze Vaktangova, Nana; Martinez Gago, Maria Dolores; Laborda Gonzalez, Belen; Garcia Alonso, Sara; Fernandez Rodriguez, Eloy
2018-05-22
Usually serum albumin is measured with dye-binding assay as bromocresol green (BCG) and bromocresol purple (BCP) methods. The aim of this paper was to examine the differences in albumin measurements between the Advia2400 BCG method (AlbBCG), Dimension RxL BCP (AlbBCP) and capillary zone electrophoresis (CZE). Albumin concentrations from 165 serum samples were analysed using AlbBCG, AlbBCP and CZE. CZE was employed to estimate different serum protein fractions. Influence of globulins on albumin concentration discrepancies between methods was estimated as well as the impact of the albumin method on aCa concentrations. Medcalc was employed for statistical analysis, setting a value of P albumin concentrations. AlbBCG were positively biased versus CZE (3.54 g/L). There was good agreement between CZE and ALbBCP (Albumin results from the BCP and BCG methods may result in unacceptable differences and clinical confusion, especially at lower albumin concentrations. Serum acute phase proteins contribute to overestimating the albumin concentration using AlbBCG.
Corcoran, Deirdre
2014-06-12
Acid elution (AE) is used to estimate foeto-maternal haemorrhage (FMH). However AE cannot differentiate between cells containing foetal or adult haemoglobin F (F cells), potentially leading to false positive results or an overestimate of the amount of FMH. The prevalence of F cells in pregnant populations remains poorly characterised. The purpose of this study was to ascertain the incidence of HbF-containing red cells in our pregnant population using anti-HbF-fluorescein isothiocyanate flow cytometry (anti-HbF FC) and to assess whether its presence leads to a significant overestimate of FMH.
Pradhan, Ajay; Ivarsson, Per; Ragnvaldsson, Daniel; Berg, Håkan; Jass, Jana; Olsson, Per-Erik
2017-04-15
Metals released into the environment continue to be of concern for human health. However, risk assessment of metal exposure is often based on total metal levels and usually does not take bioavailability data, metal speciation or matrix effects into consideration. The continued development of biological endpoint analyses are therefore of high importance for improved eco-toxicological risk analyses. While there is an on-going debate concerning synergistic or additive effects of low-level mixed exposures there is little environmental data confirming the observations obtained from laboratory experiments. In the present study we utilized qRT-PCR analysis to identify key metal response genes to develop a method for biomonitoring and risk-assessment of metal pollution. The gene expression patterns were determined for juvenile zebrafish exposed to waters from sites down-stream of a closed mining operation. Genes representing different physiological processes including stress response, inflammation, apoptosis, drug metabolism, ion channels and receptors, and genotoxicity were analyzed. The gene expression patterns of zebrafish exposed to laboratory prepared metal mixes were compared to the patterns obtained with fish exposed to the environmental samples with the same metal composition and concentrations. Exposure to environmental samples resulted in fewer alterations in gene expression compared to laboratory mixes. A biotic ligand model (BLM) was used to approximate the bioavailability of the metals in the environmental setting. However, the BLM results were not in agreement with the experimental data, suggesting that the BLM may be overestimating the risk in the environment. The present study therefore supports the inclusion of site-specific biological analyses to complement the present chemical based assays used for environmental risk-assessment. Copyright © 2017 Elsevier B.V. All rights reserved.
Arora, Shreya; Malik, Javed N.
2017-12-01
The Himalaya is one of the most seismically active regions of the world. The occurrence of several large magnitude earthquakes viz. 1905 Kangra earthquake (Mw 7.8), 1934 Bihar-Nepal earthquake (Mw 8.2), 1950 Assam earthquake (Mw 8.4), 2005 Kashmir (Mw 7.6), and 2015 Gorkha (Mw 7.8) are the testimony to ongoing tectonic activity. In the last few decades, tremendous efforts have been made along the Himalayan arc to understand the patterns of earthquake occurrences, size, extent, and return periods. Some of the large magnitude earthquakes produced surface rupture, while some remained blind. Furthermore, due to the incompleteness of the earthquake catalogue, a very few events can be correlated with medieval earthquakes. Based on the existing paleoseismic data certainly, there exists a complexity to precisely determine the extent of surface rupture of these earthquakes and also for those events, which occurred during historic times. In this paper, we have compiled the paleo-seismological data and recalibrated the radiocarbon ages from the trenches excavated by previous workers along the entire Himalaya and compared earthquake scenario with the past. Our studies suggest that there were multiple earthquake events with overlapping surface ruptures in small patches with an average rupture length of 300 km limiting Mw 7.8-8.0 for the Himalayan arc, rather than two or three giant earthquakes rupturing the whole front. It has been identified that the large magnitude Himalayan earthquakes, such as 1905 Kangra, 1934 Bihar-Nepal, and 1950 Assam, that have occurred within a time frame of 45 years. Now, if these events are dated, there is a high possibility that within the range of ±50 years, they may be considered as the remnant of one giant earthquake rupturing the entire Himalayan arc. Therefore, leading to an overestimation of seismic hazard scenario in Himalaya.
Ni, Xiangyin; Yang, Wanqin; Qi, Zemin; Liao, Shu; Xu, Zhenfeng; Tan, Bo; Wang, Bin; Wu, Qinggui; Fu, Changkun; You, Chengming; Wu, Fuzhong
2017-08-01
Experiments and models have led to a consensus that there is positive feedback between carbon (C) fluxes and climate warming. However, the effect of warming may be altered by regional and global changes in nitrogen (N) and rainfall levels, but the current understanding is limited. Through synthesizing global data on soil C pool, input and loss from experiments simulating N deposition, drought and increased precipitation, we quantified the responses of soil C fluxes and equilibrium to the three single factors and their interactions with warming. We found that warming slightly increased the soil C input and loss by 5% and 9%, respectively, but had no significant effect on the soil C pool. Nitrogen deposition alone increased the soil C input (+20%), but the interaction of warming and N deposition greatly increased the soil C input by 49%. Drought alone decreased the soil C input by 17%, while the interaction of warming and drought decreased the soil C input to a greater extent (-22%). Increased precipitation stimulated the soil C input by 15%, but the interaction of warming and increased precipitation had no significant effect on the soil C input. However, the soil C loss was not significantly affected by any of the interactions, although it was constrained by drought (-18%). These results implied that the positive C fluxes-climate warming feedback was modulated by the changing N and rainfall regimes. Further, we found that the additive effects of [warming × N deposition] and [warming × drought] on the soil C input and of [warming × increased precipitation] on the soil C loss were greater than their interactions, suggesting that simple additive simulation using single-factor manipulations may overestimate the effects on soil C fluxes in the real world. Therefore, we propose that more multifactorial experiments should be considered in studying Earth systems. © 2016 John Wiley & Sons Ltd.
Aragão, Florbela; Moreira, Maria Helena; Gabriel, Ronaldo Eugénio; Abrantes, Catarina Gavião
2013-11-01
The purpose of this study was to examine the heart rate reserve (HRR) at first and second ventilatory thresholds (VT's) in postmenopausal women and compare it with optimal intensity range recommended by the ACSM (40-84%HRR). An additional aim was to evaluate whether a higher aerobic power level corresponded to a higher HRR at VT's. Fifty-eight postmenopausal women participated in this study (aged 48-69). A graded 25 Wmin(-2) cycle ergometer (Monark E839) exercise protocol was performed in order to assess aerobic power. The heart rate and gas-exchange variables were measured continuously using a portable gas analyzer system (Cosmed K4b). The first (VT1) and the second (VT2) VT's were determined by the time course curves of ventilation and O2 and CO2 ventilatory equivalents. A K-means clustering analysis was used in order to identify VO2max groups (cut-off of 30.5 mlkg(-1)min(-1)) and differences were evaluated by an independent sample t-test. Bland-Altman plots were performed to illustrate the agreement between methods. The women's HRR values at VT1 were similar to 40% HRR in both VO2max groups. At VT2 both VO2max groups exhibited negative differences (Plower VO2max group and -16.32% in the higher VO2max group). An upper limit of 84% overestimates the %HRR value for the second ventilatory threshold, suggesting that the cardiorespiratory target zone for this population should be lower and narrower (40-70%HRR). Copyright © 2012 Sports Medicine Australia. Published by Elsevier Ltd. All rights reserved.
Blakley, G. R.
1982-01-01
Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)
Handbook of integral equations
Polyanin, Andrei D
2008-01-01
This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.
Joseph, A.; VijayKumar, K.; Desa, E.S.; Desa, E.; Peshwe, V.B.
at the mouth of the Zuari estuary, and anomalies were reported at all periods except during peak summer and the onset of the summer monsoon. These anomalies lead to an over-estimation of sea level by a tide-well based gauge. The density difference, delta p...
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
Uraltseva, N N
1995-01-01
This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p
Lebedev, D.R.
1979-01-01
Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown
Fractional Schroedinger equation
Laskin, Nick
2002-01-01
Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Ichiguchi, Katsuji
1998-01-01
A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Lacny, Sarah; Wilson, Todd; Clement, Fiona; Roberts, Derek J; Faris, Peter; Ghali, William A; Marshall, Deborah A
2018-01-01
Kaplan-Meier survival analysis overestimates cumulative incidence in competing risks (CRs) settings. The extent of overestimation (or its clinical significance) has been questioned, and CRs methods are infrequently used. This meta-analysis compares the Kaplan-Meier method to the cumulative incidence function (CIF), a CRs method. We searched MEDLINE, EMBASE, BIOSIS Previews, Web of Science (1992-2016), and article bibliographies for studies estimating cumulative incidence using the Kaplan-Meier method and CIF. For studies with sufficient data, we calculated pooled risk ratios (RRs) comparing Kaplan-Meier and CIF estimates using DerSimonian and Laird random effects models. We performed stratified meta-analyses by clinical area, rate of CRs (CRs/events of interest), and follow-up time. Of 2,192 identified abstracts, we included 77 studies in the systematic review and meta-analyzed 55. The pooled RR demonstrated the Kaplan-Meier estimate was 1.41 [95% confidence interval (CI): 1.36, 1.47] times higher than the CIF. Overestimation was highest among studies with high rates of CRs [RR = 2.36 (95% CI: 1.79, 3.12)], studies related to hepatology [RR = 2.60 (95% CI: 2.12, 3.19)], and obstetrics and gynecology [RR = 1.84 (95% CI: 1.52, 2.23)]. The Kaplan-Meier method overestimated the cumulative incidence across 10 clinical areas. Using CRs methods will ensure accurate results inform clinical and policy decisions. Copyright © 2017 Elsevier Inc. All rights reserved.
Zhalij, Alexander
2002-01-01
We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field
Functional equations with causal operators
Corduneanu, C
2003-01-01
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Differential equations for dummies
Holzner, Steven
2008-01-01
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
Degenerate nonlinear diffusion equations
Favini, Angelo
2012-01-01
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...
K. Banoo
1998-01-01
equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.
Solving Ordinary Differential Equations
Krogh, F. T.
1987-01-01
Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.
Reactimeter dispersion equation
A.G. Yuferov
2016-01-01
The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...
Differential equations I essentials
REA, Editors of
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.
Laenen, E.
1995-01-01
We propose a new evolution equation for the gluon density relevant for the region of small x B . It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists of taking shadowing effects more comprehensively into account by including multigluon correlations, and allowing for an arbitrary initial gluon distribution in a hadron. We solve the new equation for fixed α s . We find that the effects of multigluon correlations on the deep-inelastic structure function are small. (orig.)
Elsey, Helen; Owiredu, Elizabeth; Thomson, Heather; Mann, Gemma; Mehta, Rashesh; Siddiqi, Kamran
2015-02-01
Social norms approaches (SNA) are based on the premise that we frequently overestimate risk behaviours among our peers. By conducting campaigns to reduce these misperceptions, SNAs aim to reduce risk behaviours. This study examines the extent to which 12 to 13year old pupils overestimate smoking among their peers and explores the appropriateness of using SNA in secondary schools to prevent smoking uptake. The extent of overestimation of smoking among peers was assessed through an on-line SNA questionnaire in five schools (n=595). Based on questionnaire results, pupils developed SNA campaigns in each school. Qualitative methods of focus groups (7), interviews (7) and observation were used to explore in-depth, from the perspective of staff and pupils, the appropriateness and feasibility of the SNA to prevent smoking uptake in secondary schools. A quarter of pupils, 25.9% (95% CI 25.6% to 26.1%) believed that most of their peers smoked, however, only 3% (95% CI 2.8% to 3.3%) reported that they actually did; a difference of 22.9% (95% CI 19.1% to 26.6%). Self-reported smoking was not significantly different between schools (X(2)=8.7 p=0.064), however, perceptions of year group smoking was significantly different across schools (X(2)=63.9 psmoking among peers in secondary schools, thus supporting a key premise of social norms theory. Implementing SNAs and studying effects is feasible within secondary schools. Copyright © 2014 Elsevier Ltd. All rights reserved.
Manca, V.; Salibra, A.; Scollo, Giuseppe
1990-01-01
Equational type logic is an extension of (conditional) equational logic, that enables one to deal in a single, unified framework with diverse phenomena such as partiality, type polymorphism and dependent types. In this logic, terms may denote types as well as elements, and atomic formulae are either
Alternative equations of gravitation
Pinto Neto, N.
1983-01-01
It is shown, trough a new formalism, that the quantum fluctuation effects of the gravitational field in Einstein's equations are analogs to the effects of a continuum medium in Maxwell's Electrodynamics. Following, a real example of the applications of these equations is studied. Qunatum fluctuations effects as perturbation sources in Minkowski and Friedmann Universes are examined. (L.C.) [pt
Yagi, M. [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Horton, W. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies
1993-11-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite {beta} that we solve the perpendicular component of Ohm`s law to conserve the physical energy while ensuring the relation {del} {center_dot} j = 0.
Yagi, M.; Horton, W.
1993-11-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that we solve the perpendicular component of Ohm's law to conserve the physical energy while ensuring the relation ∇ · j = 0
Yagi, M.; Horton, W.
1994-01-01
A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that the perpendicular component of Ohm's law be solved to ensure ∇·j=0 for energy conservation
The currently proposed model compaction equation was derived from data sourced from the. Niger Delta and it relates porosity to depth for sandstones under hydrostatic pressure condition. The equation is useful in predicting porosity and compaction trend in hydrostatic sands of the. Niger Delta. GEOLOGICAL SETTING OF ...
M. Hazewinkel (Michiel)
1995-01-01
textabstractDedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an
The generalized Fermat equation
Beukers, F.
2006-01-01
This article will be devoted to generalisations of Fermat’s equation xn + yn = zn. Very soon after the Wiles and Taylor proof of Fermat’s Last Theorem, it was wondered what would happen if the exponents in the three term equation would be chosen differently. Or if coefficients other than 1 would
Henriksen, Jens Henrik Sahl; Brøchner-Mortensen, J; Malchow-Møller, A
1980-01-01
The total plasma (Clt) and the renal plasma (Clr) clearances of [51Cr]EDTA were determined simultaneously in nine patients with ascites due to liver cirrhosis. Clt (mean 78 ml/min, range 34-115 ml/min) was significantly higher than Clr (mean 52 ml/min, range 13-96 ml/min, P ... fluid-plasma activity ratio of [51Cr]EDTA increased throughout the investigation period (5h). The results suggest that [51Cr]EDTA equilibrates slowly with the peritoneal space which indicates that Clt will over-estimate the glomerular filtration rate by approximately 20 ml/min in patients with ascites...
J. R. Dolan,
2005-01-01
Full Text Available According to a recent global analysis, microzooplankton grazing is surprisingly invariant, ranging only between 59 and 74% of phytoplankton primary production across systems differing in seasonality, trophic status, latitude, or salinity. Thus an important biological process in the world ocean, the daily consumption of recently fixed carbon, appears nearly constant. We believe this conclusion is an artefact because dilution experiments are 1 prone to providing over-estimates of grazing rates and 2 unlikely to furnish evidence of low grazing rates. In our view the overall average rate of microzooplankton grazing probably does not exceed 50% of primary production and may be even lower in oligotrophic systems.
Löbl, Ivan
2014-02-27
Since the 1992 Rio Convention on Biological Diversity, the earth's biodiversity is a matter of constant public interest, but the community of scientists who describe and delimit species in mega-diverse animal groups, i.e. the bulk of global biodiversity, faces ever-increasing impediments. The problems are rooted in poor understanding of specificity of taxonomy, and overestimation of quantitative approaches and modern technology. A high proportion of the animal species still remains to be discovered and studied, so a more balanced approach to the situation is needed.
Applied partial differential equations
Logan, J David
2004-01-01
This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...
Brody, S; Costa, R M
2009-12-01
Research shows that (1) greater use of immature psychological defence mechanisms (associated with psychopathology) is associated with lesser orgasmic consistency from penile-vaginal intercourse (PVI), but greater frequency of other sexual behaviours and greater condom use for PVI, and (2) unlike the vectors of receptive anal intercourse and punctures, HIV acquisition during PVI is extremely unlikely in reasonably healthy persons. However, the relationship between overestimation of AIDS deaths due to 'heterosexual transmission' (often misunderstood as only PVI), sexual behaviour and mental health has been lacking. Two hundred and twenty-one Scottish women completed the Defense Style Questionnaire, reported past month frequencies of their various sexual activities, and estimated the total number of women who died from AIDS in Scotland nominally as a result of heterosexual transmission in the UK from a partner not known to be an injecting drug user, bisexual or infected through transfusion. The average respondent overestimated by 226,000%. Women providing lower estimates were less likely to use immature psychological defences, and had a lower frequency of orgasms from clitoral masturbation during PVI and from vibrator use. The results indicate that those who perceive 'heterosexual transmission' led to many AIDS deaths have poorer psychological functioning, and might be less able to appreciate PVI.
Moritz, Steffen; Pohl, Rüdiger F
2009-11-01
Overestimation of threat (OET) has been implicated in the pathogenesis of obsessive-compulsive disorder (OCD). The present study deconstructed this complex concept and looked for specific deviances in OCD relative to controls. A total of 46 participants with OCD and 51 nonclinical controls were asked: (a) to estimate the incidence rate for 20 events relating to washing, checking, positive, or negative incidents. Furthermore, they were required (b) to assess their personal vulnerability to experience each event type, and (c) to judge the degree of accompanying worry. Later, participants were confronted with the correct statistics and asked (d) to rate their degree of worry versus relief. OCD participants did not provide higher estimates for OCD-related events than healthy participants, thus rendering a knowledge deficit unlikely. The usual unrealistic optimism bias was found in both groups but was markedly attenuated in OCD participants. OCD-related events worried OCD participants more than controls. Confrontation with the correct statistics appeased OCD participants less than healthy participants. Even in the case of large initial overestimations for OCD-related events, correct information appeased OCD participants significantly less than healthy participants. Our results suggest that OCD is not associated with a knowledge deficit regarding OCD-related events but that patients feel personally more vulnerable than nonclinical controls.
Hyperbolic partial differential equations
Witten, Matthew
1986-01-01
Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M
Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning
2001-01-01
Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which
Differential equations problem solver
Arterburn, David R
2012-01-01
REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and
Supersymmetric quasipotential equations
Zaikov, R.P.
1981-01-01
A supersymmetric extension of the Logunov-Tavkhelidze quasipotential approach is suggested. The supersymmetric Bethe- Salpeter equation is an initial equation. The transition from the four-time to the two-time Green function is made in the super- center-of-mass system. The two-time Green function has no inverse function in the whole spinor space. The resolvent operator if found using the Majorana character of the spinor wave function. The supersymmetric quasipotential equation is written. The consideration is carried out in the framework of the theory of chiral scalar superfields [ru
Local instant conservation equations
Delaje, Dzh.
1984-01-01
Local instant conservation equations for two-phase flow are derived. Derivation of the equation starts from the recording of integral laws of conservation for a fixed reference volume, containing both phases. Transformation of the laws, using the Leibniz rule and Gauss theory permits to obtain the sum of two integrals as to the volume and integral as to the surface. Integrals as to the volume result in local instant differential equations, in particular derivatives for each phase, and integrals as to the surface reflect local instant conditions of a jump on interface surface
Beginning partial differential equations
O'Neil, Peter V
2011-01-01
A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres
Ordinary differential equations
Miller, Richard K
1982-01-01
Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,
Uncertain differential equations
Yao, Kai
2016-01-01
This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.
Applied partial differential equations
Logan, J David
2015-01-01
This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...
Nonlinear differential equations
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.
Tsintsadze, Nodar L.; Tsintsadze, Levan N.
2008-01-01
A general derivation of the charging equation of a dust grain is presented, and indicated where and when it can be used. A problem of linear fluctuations of charges on the surface of the dust grain is discussed.
Equations For Rotary Transformers
Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.
1988-01-01
Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.
Problems in differential equations
Brenner, J L
2013-01-01
More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.
Applied partial differential equations
DuChateau, Paul
2012-01-01
Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.
Nonlinear differential equations
Dresner, L.
1988-01-01
This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics
Saaty, Thomas L
1981-01-01
Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.
SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER
Collier, D.M.; Meeks, L.A.; Palmer, J.P.
1960-05-10
A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.
Structural Equations and Causation
Hall, Ned
2007-01-01
Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.
Equations of radiation hydrodynamics
Mihalas, D.
1982-01-01
The purpose of this paper is to give an overview of the role of radiation in the transport of energy and momentum in a combined matter-radiation fluid. The transport equation for a moving radiating fluid is presented in both a fully Eulerian and a fully Lagrangian formulation, along with conservation equations describing the dynamics of the fluid. Special attention is paid to the problem of deriving equations that are mutually consistent in each frame, and between frames, to 0(v/c). A detailed analysis is made to show that in situations of broad interest, terms that are formally of 0(v/c) actually dominate the solution, demonstrating that it is esential (1) to pay scrupulous attention to the question of the frame dependence in formulating the equations; and (2) to solve the equations to 0(v/c) in quite general circumstances. These points are illustrated in the context of the nonequilibrium radiation diffusion limit, and a sketch of how the Lagrangian equations are to be solved will be presented
Quantum linear Boltzmann equation
Vacchini, Bassano; Hornberger, Klaus
2009-01-01
We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.
Covariant field equations in supergravity
Vanhecke, Bram [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium); Ghent University, Faculty of Physics, Gent (Belgium); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)
2017-12-15
Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Covariant field equations in supergravity
Vanhecke, Bram; Proeyen, Antoine van
2017-01-01
Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Differential Equation over Banach Algebra
Kleyn, Aleks
2018-01-01
In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.
An artificial neural network to predict resting energy expenditure in obesity.
Disse, Emmanuel; Ledoux, Séverine; Bétry, Cécile; Caussy, Cyrielle; Maitrepierre, Christine; Coupaye, Muriel; Laville, Martine; Simon, Chantal
2017-09-01
The resting energy expenditure (REE) determination is important in nutrition for adequate dietary prescription. The gold standard i.e. indirect calorimetry is not available in clinical settings. Thus, several predictive equations have been developed, but they lack of accuracy in subjects with extreme weight including obese populations. Artificial neural networks (ANN) are useful predictive tools in the area of artificial intelligence, used in numerous clinical fields. The aim of this study was to determine the relevance of ANN in predicting REE in obesity. A Multi-Layer Perceptron (MLP) feed-forward neural network with a back propagation algorithm was created and cross-validated in a cohort of 565 obese subjects (BMI within 30-50 kg m -2 ) with weight, height, sex and age as clinical inputs and REE measured by indirect calorimetry as output. The predictive performances of ANN were compared to those of 23 predictive REE equations in the training set and in two independent sets of 100 and 237 obese subjects for external validation. Among the 23 established prediction equations for REE evaluated, the Harris & Benedict equations recalculated by Roza were the most accurate for the obese population, followed by the USA DRI, Müller and the original Harris & Benedict equations. The final 5-fold cross-validated three-layer 4-3-1 feed-forward back propagation ANN model developed in that study improved precision and accuracy of REE prediction over linear equations (precision = 68.1%, MAPE = 8.6% and RMSPE = 210 kcal/d), independently from BMI subgroups within 30-50 kg m -2 . External validation confirmed the better predictive performances of ANN model (precision = 73% and 65%, MAPE = 7.7% and 8.6%, RMSPE = 187 kcal/d and 200 kcal/d in the 2 independent datasets) for the prediction of REE in obese subjects. We developed and validated an ANN model for the prediction of REE in obese subjects that is more precise and accurate than established REE predictive
Mohie Aldeen Abd Alzaher Khalifa
2016-10-01
Conclusions: The present study supports on-HCT as a reliable, on-invasive and continuous methods determining the requirement for in-flight O2 are relatively constant. Predictive equations considerably overestimate the need for in-flight O2 compared to hypoxic inhalation test. Predictive equations are cheap, readily available methods of flight assessment, but this study shows poor agreement between their predictions and the measured individual hypoxic responses during HCT.
Estimate of body composition by Hume's equation: validation with DXA.
Carnevale, Vincenzo; Piscitelli, Pamela Angela; Minonne, Rita; Castriotta, Valeria; Cipriani, Cristiana; Guglielmi, Giuseppe; Scillitani, Alfredo; Romagnoli, Elisabetta
2015-05-01
We investigated how the Hume's equation, using the antipyrine space, could perform in estimating fat mass (FM) and lean body mass (LBM). In 100 (40 male ad 60 female) subjects, we estimated FM and LBM by the equation and compared these values with those measured by a last generation DXA device. The correlation coefficients between measured and estimated FM were r = 0.940 (p LBM were r = 0.913 (p LBM, though the equation underestimated FM and overestimated LBM in respect to DXA. The mean difference for FM was 1.40 kg (limits of agreement of -6.54 and 8.37 kg). For LBM, the mean difference in respect to DXA was 1.36 kg (limits of agreement -8.26 and 6.52 kg). The root mean square error was 3.61 kg for FM and 3.56 kg for LBM. Our results show that in clinically stable subjects the Hume's equation could reliably assess body composition, and the estimated FM and LBM approached those measured by a modern DXA device.
Momentum equation for arc-driven rail guns
Batteh, J.H.
1984-01-01
In several models of arc-driven rail guns, the rails are assumed to be infinitely high to simplify the calculation of the electromagnetic fields which appear in the momentum equation for the arc. This assumption leads to overestimates of the arc pressures and accelerations by approximately a factor of 2 for typical rail-gun geometries. In this paper, we develop a simple method for modifying the momentum equation to account for the effect of finite-height rails on the performance of the rail gun and the properties of the arc. The modification is based on an integration of the Lorentz force across the arc cross section at each axial location in the arc. Application of this technique suggests that, for typical rail-gun geometries and moderately long arcs, the momentum equation appropriate for infinite-height rails can be retained provided that the magnetic pressure term in the equation is scaled by a factor which depends on the effective inductance of the gun. The analysis also indicates that the magnetic pressure gradient actually changes sign near the arc/projectile boundary because of the magnetic fields associated with the arc current
Transport equation solving methods
Granjean, P.M.
1984-06-01
This work is mainly devoted to Csub(N) and Fsub(N) methods. CN method: starting from a lemma stated by Placzek, an equivalence is established between two problems: the first one is defined in a finite medium bounded by a surface S, the second one is defined in the whole space. In the first problem the angular flux on the surface S is shown to be the solution of an integral equation. This equation is solved by Galerkin's method. The Csub(N) method is applied here to one-velocity problems: in plane geometry, slab albedo and transmission with Rayleigh scattering, calculation of the extrapolation length; in cylindrical geometry, albedo and extrapolation length calculation with linear scattering. Fsub(N) method: the basic integral transport equation of the Csub(N) method is integrated on Case's elementary distributions; another integral transport equation is obtained: this equation is solved by a collocation method. The plane problems solved by the Csub(N) method are also solved by the Fsub(N) method. The Fsub(N) method is extended to any polynomial scattering law. Some simple spherical problems are also studied. Chandrasekhar's method, collision probability method, Case's method are presented for comparison with Csub(N) and Fsub(N) methods. This comparison shows the respective advantages of the two methods: a) fast convergence and possible extension to various geometries for Csub(N) method; b) easy calculations and easy extension to polynomial scattering for Fsub(N) method [fr
Introduction to partial differential equations
Greenspan, Donald
2000-01-01
Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.
Wang, Fumin; Gonsamo, Alemu; Chen, Jing M; Black, T Andrew; Zhou, Bin
2014-11-01
Daily canopy photosynthesis is usually temporally upscaled from instantaneous (i.e., seconds) photosynthesis rate. The nonlinear response of photosynthesis to meteorological variables makes the temporal scaling a significant challenge. In this study, two temporal upscaling schemes of daily photosynthesis, the integrated daily model (IDM) and the segmented daily model (SDM), are presented by considering the diurnal variations of meteorological variables based on a coupled photosynthesis-stomatal conductance model. The two models, as well as a simple average daily model (SADM) with daily average meteorological inputs, were validated using the tower-derived gross primary production (GPP) to assess their abilities in simulating daily photosynthesis. The results showed IDM closely followed the seasonal trend of the tower-derived GPP with an average RMSE of 1.63 g C m(-2) day(-1), and an average Nash-Sutcliffe model efficiency coefficient (E) of 0.87. SDM performed similarly to IDM in GPP simulation but decreased the computation time by >66%. SADM overestimated daily GPP by about 15% during the growing season compared to IDM. Both IDM and SDM greatly decreased the overestimation by SADM, and improved the simulation of daily GPP by reducing the RMSE by 34 and 30%, respectively. The results indicated that IDM and SDM are useful temporal upscaling approaches, and both are superior to SADM in daily GPP simulation because they take into account the diurnally varying responses of photosynthesis to meteorological variables. SDM is computationally more efficient, and therefore more suitable for long-term and large-scale GPP simulations.
Universal equation for estimating ideal body weight and body weight at any BMI.
Peterson, Courtney M; Thomas, Diana M; Blackburn, George L; Heymsfield, Steven B
2016-05-01
Ideal body weight (IBW) equations and body mass index (BMI) ranges have both been used to delineate healthy or normal weight ranges, although these 2 different approaches are at odds with each other. In particular, past IBW equations are misaligned with BMI values, and unlike BMI, the equations have failed to recognize that there is a range of ideal or target body weights. For the first time, to our knowledge, we merged the concepts of a linear IBW equation and of defining target body weights in terms of BMI. With the use of calculus and approximations, we derived an easy-to-use linear equation that clinicians can use to calculate both IBW and body weight at any target BMI value. We measured the empirical accuracy of the equation with the use of NHANES data and performed a comparative analysis with past IBW equations. Our linear equation allowed us to calculate body weights for any BMI and height with a mean empirical accuracy of 0.5-0.7% on the basis of NHANES data. Moreover, we showed that our body weight equation directly aligns with BMI values for both men and women, which avoids the overestimation and underestimation problems at the upper and lower ends of the height spectrum that have plagued past IBW equations. Our linear equation increases the sophistication of IBW equations by replacing them with a single universal equation that calculates both IBW and body weight at any target BMI and height. Therefore, our equation is compatible with BMI and can be applied with the use of mental math or a calculator without the need for an app, which makes it a useful tool for both health practitioners and the general public. © 2016 American Society for Nutrition.
Quadratic Diophantine equations
Andreescu, Titu
2015-01-01
This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Boussinesq evolution equations
Bredmose, Henrik; Schaffer, H.; Madsen, Per A.
2004-01-01
This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...
Anon.
1982-01-01
The way nuclear power plants are built practically excludes accidents with serious consequences. This is attended to by careful selection of material, control of fabrication and regular retesting as well as by several safety systems working independently. But the remaining risk, a 'hypothetic' uncontrollable incident with catastrophic effects is the main subject of the discussion on the peaceful utilization of nuclear power. The this year's 'Annual Meeting on Nuclear Engineering' in Mannheim and the meeting 'Reactor Safety Research' in Cologne showed, that risk studies so far were too pessimistic. 'Best estimate' calculations suggest that core melt-down accidents only occur if almost all safety systems fail, that accidents take place much more slowly, and that the release of radioactive fission products is by several magnitudes lower than it was assumed until now. (orig.) [de
Equations of mathematical physics
Tikhonov, A N
2011-01-01
Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri
Iteration of adjoint equations
Lewins, J.D.
1994-01-01
Adjoint functions are the basis of variational methods and now widely used for perturbation theory and its extension to higher order theory as used, for example, in modelling fuel burnup and optimization. In such models, the adjoint equation is to be solved in a critical system with an adjoint source distribution that is not zero but has special properties related to ratios of interest in critical systems. Consequently the methods of solving equations by iteration and accumulation are reviewed to show how conventional methods may be utilized in these circumstances with adequate accuracy. (author). 3 refs., 6 figs., 3 tabs
Systematic Equation Formulation
Lindberg, Erik
2007-01-01
A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....
Partial differential equations
Agranovich, M S
2002-01-01
Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplectic geometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and gener
Generalized estimating equations
Hardin, James W
2002-01-01
Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Analysis of wave equation in electromagnetic field by Proca equation
Pamungkas, Oky Rio; Soeparmi; Cari
2017-01-01
This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)
Comparison of Kernel Equating and Item Response Theory Equating Methods
Meng, Yu
2012-01-01
The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…
Test equating methods and practices
Kolen, Michael J
1995-01-01
In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...
Kuehl, Joseph
2016-11-01
The parabolized stability equations (PSE) have been developed as an efficient and powerful tool for studying the stability of advection-dominated laminar flows. In this work, a new "wavepacket" formulation of the PSE is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening and results in disturbance saturation amplitudes consistent with experiment. A Mach 6 flared-cone example is presented. Support from the AFOSR Young Investigator Program via Grant FA9550-15-1-0129 is gratefully acknowledges.
The Raychaudhuri equation is central to the understanding of gravitational attraction in ... of K Gödel on the ideas of shear and vorticity in cosmology (he defines the shear. (eq. (8) in [1]) .... which follows from the definition of the scale factor l.
Generalized reduced magnetohydrodynamic equations
Kruger, S.E.
1999-01-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-Alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics
Calculus & ordinary differential equations
Pearson, David
1995-01-01
Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.
research, teaching and practice related to the analysis and design ... its variants, are present in a large number of ma- chines used in daily ... with advanced electronics, sensors, control systems and computing ... ted perfectly well with the rapidly developing comput- .... velopment of the Freudenstein equation using Figure 3.
Differential Equation of Equilibrium
user
ABSTRACT. Analysis of underground circular cylindrical shell is carried out in this work. The forth order differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the assumptions of P. L Pasternak. Laplace transformation was used to solve the governing ...
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and
Hatem Mejjaoli
2008-12-01
Full Text Available We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
ANTHROPOMETRIC PREDICTIVE EQUATIONS FOR ...
Keywords: Anthropometry, Predictive Equations, Percentage Body Fat, Nigerian Women, Bioelectric Impedance ... such as Asians and Indians (Pranav et al., 2009), ... size (n) of at least 3o is adjudged as sufficient for the ..... of people, gender and age (Vogel eta/., 1984). .... Fish Sold at Ile-Ife Main Market, South West Nigeria.
However, one can associate the term with any solution of nonlinear partial differential equations (PDEs) which (i) represents a wave of permanent form, (ii) is localized ... In the past several decades, many methods have been proposed for solving nonlinear PDEs, such as ... space–time fractional derivative form of eq. (1) and ...
Fay, Temple H.
2010-01-01
Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…
Guiding center drift equations
Boozer, A.H.
1979-03-01
The quations for particle guiding center drift orbits are given in a new magnetic coordinate system. This form of the equations not only separates the fast motion along the lines from the slow motion across, but also requires less information about the magnetic field than many other formulations of the problem
dimensional nonlinear evolution equations
in real-life situations, it is important to find their exact solutions. Further, in ... But only little work is done on the high-dimensional equations. .... Similarly, to determine the values of d and q, we balance the linear term of the lowest order in eq.
Stochastic nonlinear beam equations
Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan
2005-01-01
Roč. 132, č. 1 (2005), s. 119-149 ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005
Savoy, L. G.
1988-01-01
Describes a study of students' ability to balance equations. Answers to a test on this topic were analyzed to determine the level of understanding and processes used by the students. Presented is a method to teach this skill to high school chemistry students. (CW)
An Equation-of-State Compositional In-Situ Combustion Model: A Study of Phase Behavior Sensitivity
Kristensen, Morten Rode; Gerritsen, M. G.; Thomsen, Per Grove
2009-01-01
phase behavior sensitivity for in situ combustion, a thermal oil recovery process. For the one-dimensional model we first study the sensitivity to numerical discretization errors and provide grid density guidelines for proper resolution of in situ combustion behavior. A critical condition for success...... to ignition. For a particular oil we show that the simplified approach overestimates the required air injection rate for sustained front propagation by 17% compared to the equation of state-based approach....
David Herron
2008-06-01
Full Text Available Objective – The objective of this study is an investigation of the relationship between students’ self-assessment of their information literacy skills and their actual skill level, as well as an analysis of whether library anxiety is related to information skill attainment. Design – Quantitative research design (Information Literacy Test (ILT, Library Anxiety Scale (LAS, pre and post surveys.Setting – Florida State University, United States.Subjects – Students, incoming freshmen.Methods – Information literacy skills were measured using the Information Literacy Test (ILT, presenting subjects with 65 multiple choice items designed around four of the five ACRL information literacy standards, in which students were expectedto: 1 determine the nature and extent of the information needed; 2 access needed information effectively and efficiently; 3 evaluate information and its sources critically and incorporates selected information into his/her knowledge base system; 4 understand many of the economic, legal and social issues surrounding the use of information and accesses and uses information ethically and legally. The ILT categorized participant scores as non-proficient(Main Results – The main aim of the study was to test the hypothesis that students who test non-proficient on an information literacy test tend to overestimate their competency to a higher degree than proficient and advanced students. In the pre- and post-surveys, the students were asked to estimate their performance onthe ILT in terms of the expected percentage of questions they would answer correctly, the number of questions they expected to answer correctly, and how their performance on the ILT would compare toothers taking the test (in percentage. The results of the study show that all students overestimate their abilities, both in terms of performance and relative performance, in the pre-survey. The estimated percentage correct answers for the whole group was 75%, but
Lectures on partial differential equations
Petrovsky, I G
1992-01-01
Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.
Quantum equations from Brownian motions
Rajput, B.S.
2011-01-01
Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows it's classical counter part on applying Heisenberg uncertainly principle between energy and time without applying any analytical continuation. (author)
Elements of partial differential equations
Sneddon, Ian Naismith
1957-01-01
Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st
On generalized fractional vibration equation
Dai, Hongzhe; Zheng, Zhibao; Wang, Wei
2017-01-01
Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.
Methods for Equating Mental Tests.
1984-11-01
1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth
Caicedo-Eraso, J C; Gonzalez-Correa, C A; Gonzalez-Correa, C H
2013-01-01
Several studies have shown that the accuracy of BIA results depends of ethnicity, age, gender, hormonal and genetic variations and, so far, there are not specific equations for Colombian population. The purpose was to evaluate reported BIA equations to determine their usefulness in body composition assessment in young females from Colombia using hydrodensitometry as the reference method. A sample of 30 young females was evaluated. Inclusion and exclusion criteria were defined to minimize the variability of BIA. Height, weight, multi-frequency BIA, residual lung volume (RV) and underwater weight (UWW) were measured. Five BIA equations met the inclusion criteria of this study. Three equations overestimated and two equations underestimated body fat (BF). Paired Student t-test and Bland and Altman analysis (p<0.05) showed significant differences in four BIA equations. However, all standard error of estimate (SEE) to BF was greater than 2.7 kg. This study showed that the five selected BIA equations are not valid for estimation of body composition in young females from Colombia. It is recommended to develop BIA equations to improve BF fat assessment in our population.
equateIRT: An R Package for IRT Test Equating
Michela Battauz
2015-12-01
Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.
Raboisson, D; Mounié, M; Khenifar, E; Maigné, E
2015-12-01
Subclinical ketosis (SCK) is a major metabolic disorder that affects dairy cows, and its lactational prevalence in Europe is estimated to be at 25%. Nonetheless, few data are available on the economics of SCK, although its management clearly must be improved. With this in mind, this study develops a double-step stochastic approach to evaluate the total cost of SCK to dairy farming. First, all the production and reproduction changes and all the health disorders associated with SCK were quantified using the meta-analysis from a previous study. Second, the total cost of SCK was determined with a stochastic model using distribution laws as input parameters. The mean total cost of SCK was estimated to be Є257 per calving cow with SCK (95% prediction interval (PI): Є72-442). The margin over feeding costs slightly influenced the results. When the parameters of the model are not modified to account for the conclusions from the meta-analysis and for the prevalence of health disorders in the population without SCK, the mean cost of SCK was overestimated by 68%, reaching Є434 per calving cow (95%PI: Є192-676). This result indicates that the total cost of complex health disorders is likely to be substantially overestimated when calculations use raw results from the literature or-even worse-punctual data. Excluding labour costs in the estimation reduced the SCK total cost by 12%, whereas excluding contributors with scarce data and imprecise calibrations (for lameness and udder health) reduced costs by another 18-20% (Є210, 95%PI=30-390). The proposed method accounted for uncertainty and variability in inputs by using distributions instead of point estimates. The mean value and associated prediction intervals (PIs) yielded good insight into the economic consequences of this complex disease and can be easily and practically used by decision makers in the field while simultaneously accounting for biological variability. Moreover, PIs can help prevent the blind use of economic
Woo, Sang-Hee; Kwak, Kyung-Hwan; Bae, Gwi-Nam; Kim, Kyung Hwan; Kim, Chang Hyeok; Yook, Se-Jin; Jeon, Sangzin; Kwon, Sangil; Kim, Jeongsoo; Lee, Seung-Bok
2016-11-01
The unintended influence of exhaust plumes emitted from a vehicle ahead to on-road air quality surveying data measured with a mobile laboratory (ML) at 20-40 km h -1 in dense traffic areas was investigated by experiment and life-sized computational fluidic dynamics (CFD) simulation. The ML equipped with variable sampling inlets of five columns by four rows was used to measure the spatial distribution of CO 2 and NO x concentrations when following 5-20 m behind a sport utility vehicle (SUV) as an emitter vehicle equipped with a portable emission monitoring system (PEMS). The PEMS measured exhaust gases at the tailpipe for input data of the CFD simulations. After the CFD method was verified with experimental results of the SUV, dispersion of exhaust plumes emitted from a bus and a sedan was numerically analyzed. More dilution of the exhaust plume was observed at higher vehicle speeds, probably because of eddy diffusion that was proportional to turbulent kinetic energy and vehicle speed. The CO 2 and NO x concentrations behind the emitter vehicle showed less overestimation as both the distance between the two vehicles and their background concentrations increased. If the height of the ML inlet is lower than 2 m and the ML travels within 20 m behind a SUV and a sedan ahead at 20 km h -1 , the overestimation should be considered by as much as 200 ppb in NO x and 80 ppm in CO 2 . Following a bus should be avoided if possible, because effect of exhaust plumes from a bus ahead could not be negligible even when the distance between the bus and the ML with the inlet height of 2 m, was more than 40 m. Recommendations are provided to avoid the unintended influence of exhaust plumes from vehicles ahead of the ML during on-road measurement in urban dense traffic conditions. Copyright © 2016 Elsevier Ltd. All rights reserved.
Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2018-01-01
We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.
Dyre, Jeppe
1995-01-01
energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk modelthe energy master equation...... (EME)is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...
Classical Diophantine equations
1993-01-01
The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...
Flavored quantum Boltzmann equations
Cirigliano, Vincenzo; Lee, Christopher; Ramsey-Musolf, Michael J.; Tulin, Sean
2010-01-01
We derive from first principles, using nonequilibrium field theory, the quantum Boltzmann equations that describe the dynamics of flavor oscillations, collisions, and a time-dependent mass matrix in the early universe. Working to leading nontrivial order in ratios of relevant time scales, we study in detail a toy model for weak-scale baryogenesis: two scalar species that mix through a slowly varying time-dependent and CP-violating mass matrix, and interact with a thermal bath. This model clearly illustrates how the CP asymmetry arises through coherent flavor oscillations in a nontrivial background. We solve the Boltzmann equations numerically for the density matrices, investigating the impact of collisions in various regimes.
Causal electromagnetic interaction equations
Zinoviev, Yury M.
2011-01-01
For the electromagnetic interaction of two particles the relativistic causal quantum mechanics equations are proposed. These equations are solved for the case when the second particle moves freely. The initial wave functions are supposed to be smooth and rapidly decreasing at the infinity. This condition is important for the convergence of the integrals similar to the integrals of quantum electrodynamics. We also consider the singular initial wave functions in the particular case when the second particle mass is equal to zero. The discrete energy spectrum of the first particle wave function is defined by the initial wave function of the free-moving second particle. Choosing the initial wave functions of the free-moving second particle it is possible to obtain a practically arbitrary discrete energy spectrum.
Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation
Hamidreza Rezazadeh
2014-05-01
Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.
Equations of multiparticle dynamics
Chao, A.W.
1987-01-01
The description of the motion of charged-particle beams in an accelerator proceeds in steps of increasing complexity. The first step is to consider a single-particle picture in which the beam is represented as a collection on non-interacting test particles moving in a prescribed external electromagnetic field. Knowing the external field, it is then possible to calculate the beam motion to a high accuracy. The real beam consists of a large number of particles, typically 10 11 per beam bunch. It is sometimes inconvenient, or even impossible, to treat the real beam behavior using the single particle approach. One way to approach this problem is to supplement the single particle by another qualitatively different picture. The commonly used tools in accelerator physics for this purpose are the Vlasov and the Fokker-Planck equations. These equations assume smooth beam distributions and are therefore strictly valid in the limit of infinite number of micro-particles, each carrying an infinitesimal charge. The hope is that by studying the two extremes -- the single particle picture and the picture of smooth beam distributions -- we will be able to describe the behavior of our 10 11 -particle system. As mentioned, the most notable use of the smooth distribution picture is the study of collective beam instabilities. However, the purpose of this lecture is not to address this more advanced subject. Rather, it has the limited goal to familiarize the reader with the analytical tools, namely the Vlasov and the Fokker-Planck equations, as a preparation for dealing with the more advanced problems at later times. We will first derive these equations and then illustrate their applications by several examples which allow exact solutions
Electroweak evolution equations
Ciafaloni, Paolo; Comelli, Denis
2005-01-01
Enlarging a previous analysis, where only fermions and transverse gauge bosons were taken into account, we write down infrared-collinear evolution equations for the Standard Model of electroweak interactions computing the full set of splitting functions. Due to the presence of double logs which are characteristic of electroweak interactions (Bloch-Nordsieck violation), new infrared singular splitting functions have to be introduced. We also include corrections related to the third generation Yukawa couplings
Differential equations with Mathematica
Abell, Martha L
2004-01-01
The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica
Damped nonlinear Schrodinger equation
Nicholson, D.R.; Goldman, M.V.
1976-01-01
High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time
Fun with Differential Equations
IAS Admin
tion of ® with ¼=2. One can use the uniqueness of solutions of differential equations to prove the addition formulae for sin(t1 +t2), etc. But instead of continuing with this thought process, let us do something more interesting. Now we shall consider another system. Fix 0 < < 1. I am looking for three real-valued functions x(t), ...
Mathematics and Maxwell's equations
Boozer, Allen H
2010-01-01
The universality of mathematics and Maxwell's equations is not shared by specific plasma models. Computations become more reliable, efficient and transparent if specific plasma models are used to obtain only the information that would otherwise be missing. Constraints of high universality, such as those from mathematics and Maxwell's equations, can be obscured or lost by integrated computations. Recognition of subtle constraints of high universality is important for (1) focusing the design of control systems for magnetic field errors in tokamaks from perturbations that have little effect on the plasma to those that do, (2) clarifying the limits of applicability to astrophysics of computations of magnetic reconnection in fields that have a double periodicity or have B-vector =0 on a surface, as in a Harris sheet. Both require a degree of symmetry not expected in natural systems. Mathematics and Maxwell's equations imply that neighboring magnetic field lines characteristically separate exponentially with distance along a line. This remarkably universal phenomenon has been largely ignored, though it defines a trigger for reconnection through a critical magnitude of exponentiation. These and other examples of the importance of making distinctions and understanding constraints of high universality are explained.
M. Paul Gough
2008-07-01
Full Text Available LandauerÃ¢Â€Â™s principle is applied to information in the universe. Once stars began forming there was a constant information energy density as the increasing proportion of matter at high stellar temperatures exactly compensated for the expanding universe. The information equation of state was close to the dark energy value, w = -1, for a wide range of redshifts, 10 > z > 0.8, over one half of cosmic time. A reasonable universe information bit content of only 1087 bits is sufficient for information energy to account for all dark energy. A time varying equation of state with a direct link between dark energy and matter, and linked to star formation in particular, is clearly relevant to the cosmic coincidence problem. In answering the Ã¢Â€Â˜Why now?Ã¢Â€Â™ question we wonder Ã¢Â€Â˜What next?Ã¢Â€Â™ as we expect the information equation of state to tend towards w = 0 in the future.c
Generalized reduced MHD equations
Kruger, S.E.; Hegna, C.C.; Callen, J.D.
1998-07-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson
Salvo, Francesco; Lonati, Chiara; Albano, Monica; Fogliacco, Paolo; Errani, Andrea Riccardo; Vallo, Cinzia; Berardi, Michele; Meinero, Vito; Muzzulini, Carlo Lorenzo; Morganti, Alberto
2016-09-01
Alarm reaction to clinical blood pressure (BP) measurement, defined white-coat effect (WCE), can cause overestimation of true BP values. To assess whether ambulatory blood pressure monitoring (ABPM) can similarly affect BP values during the initial hours of recording. In 420 ABPMs selected for a first systolic BP (SBP) reading at least 10 mmHg higher than the mean daytime SBP, we calculated mean diurnal and 24 h SBP with and without the exclusion of the two first hours of recording defined as the WCE window (WCEw). We also calculated the magnitude and duration of WCE. These analyses were also performed separately in patients off anti-hypertensive treatment (n = 156), and on treatment with and without the inclusion of beta-blockers (respectively n = 113 and 151). Exclusion of WCEw period reduced mean diurnal and 24 h SBP respectively from 135 ± 0.5 to 133 ± 0.5 (p ABPM is not free from WCE. WCE may affect the overall estimation of BP profile and is longer but less blunted by beta-blockers in females than in males.
Hirami, Ryouichi; Iwasaki, Kohichiro; Kusachi, Shozo; Murakami, Takashi; Hina, Kazuyoshi; Matano, Shigeru; Murakami, Masaaki; Kita, Toshimasa; Sakakibara, Noburu; Tsuji, Takao
2000-01-01
Purpose: To examine changes in the reference segment luminal diameter after coronary angioplasty.Methods: Sixty-one patients with stable angina pectoris or old myocardial infarction were examined. Coronary angiograms were recorded before coronary angioplasty (pre-angioplasty) and immediately after (post-angioplasty), as well as 3 months after. Artery diameters were measured on cine-film using quantitative coronary angiographic analysis.Results: The diameters of the proximal segment not involved in the balloon inflation and segments in the other artery did not change significantly after angioplasty, but the reference segment diameter significantly decreased (4.7%). More than 10% luminal reduction was observed in seven patients (11%) and more than 5% reduction was observed in 25 patients (41%). More than 5% underestimation of the stenosis was observed in 22 patients (36%) when the post-angioplasty reference diameter was used as the reference diameter, compared with when the pre-angioplasty measurement was used and more than 10% underestimation was observed in five patients (8%).Conclusion: This study indicated that evaluation by percent diameter stenosis, with the reference diameter from immediately after angioplasty, overestimates the dilative effects of coronary angioplasty, and that it is thus better to evaluate the efficacy of angioplasty using the absolute diameter in addition to percent luminal stenosis
Computing generalized Langevin equations and generalized Fokker-Planck equations.
Darve, Eric; Solomon, Jose; Kia, Amirali
2009-07-07
The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.
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plant made of 12mm thick steel plate was used in de steel plate ... water treatment plant. ... ameters affecting filtration processes were used to derive an equation usin ..... system. However, in deriving the equation onl terms are incorporated.
Reduction operators of Burgers equation.
Pocheketa, Oleksandr A; Popovych, Roman O
2013-02-01
The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.
Auxiliary equation method for solving nonlinear partial differential equations
Sirendaoreji,; Jiong, Sun
2003-01-01
By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation
Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating
Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen
2012-01-01
This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…
Differential Equations as Actions
Ronkko, Mauno; Ravn, Anders P.
1997-01-01
We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...... actions shall terminate. It is shown that the proposed differential action has a semantics which corresponds to a discrete approximation when the discrete step size goes to zero. The extension gives action systems the power to model real-time clocks and continuous evolutions within hybrid systems....
Partial differential equations
Levine, Harold
1997-01-01
The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.
Ordinary differential equations
Cox, William
1995-01-01
Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further
Partial differential equations
Sloan, D; Süli, E
2001-01-01
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in
Elliptic partial differential equations
Han, Qing
2011-01-01
Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things abo
Ted W. Sammis
2013-09-01
Full Text Available Net radiation is a key component of the energy balance, whose estimation accuracy has an impact on energy flux estimates from satellite data. In typical remote sensing evapotranspiration (ET algorithms, the outgoing shortwave and longwave components of net radiation are obtained from remote sensing data, while the incoming shortwave (RS and longwave (RL components are typically estimated from weather data using empirical equations. This study evaluates the accuracy of empirical equations commonly used in remote sensing ET algorithms for estimating RS and RL radiation. Evaluation is carried out through comparison of estimates and observations at five sites that represent different climatic regions from humid to arid. Results reveal (1 both RS and RL estimates from all evaluated equations well correlate with observations (R2 ≥ 0.92, (2 RS estimating equations tend to overestimate, especially at higher values, (3 RL estimating equations tend to give more biased values in arid and semi-arid regions, (4 a model that parameterizes the diffuse component of radiation using two clearness indices and a simple model that assumes a linear increase of atmospheric transmissivity with elevation give better RS estimates, and (5 mean relative absolute errors in the net radiation (Rn estimates caused by the use of RS and RL estimating equations varies from 10% to 22%. This study suggests that Rn estimates using recommended incoming radiation estimating equations could improve ET estimates.
dimensional Jaulent–Miodek equations
(2+1)-dimensional Jaulent–Miodek equation; the first integral method; kinks; ... and effective method for solving nonlinear partial differential equations which can ... of the method employed and exact kink and soliton solutions are constructed ...
Equationally Noetherian property of Ershov algebras
Dvorzhetskiy, Yuriy
2014-01-01
This article is about equationally Noetherian and weak equationally Noetherian property of Ershov algebras. Here we show two canonical forms of the system of equations over Ershov algebras and two criteria of equationally Noetherian and weak equationally Noetherian properties.
de Luis, D A; Aller, R; Izaola, O; Romero, E
2006-01-01
The aim of our study was to evaluate the accuracy of the equations to estimate REE in obese patents and develop a new equation in our obese population. A population of 200 obesity outpatients was analyzed in a prospective way. The following variables were specifically recorded: age, weight, body mass index (BMI), waist circumference, and waist-to-hip ratio. Basal glucose, insulin, and TSH (thyroid-stimulating hormone) were measured. An indirect calorimetry and a tetrapolar electrical bioimpedance were performed. REE measured by indirect calorimetry was compared with REE obtained by prediction equations to obese or nonobese patients. The mean age was 44.8 +/- 16.81 years and the mean BMI 34.4 +/- 5.3. Indirect calorimetry showed that, as compared to women, men had higher resting energy expenditure (REE) (1,998.1 +/- 432 vs. 1,663.9 +/- 349 kcal/day; p consumption (284.6 +/- 67.7 vs. 238.6 +/- 54.3 ml/min; p predicted by prediction equations showed the next data; Berstein's equation (r = 0.65; p prediction equation was REE = 58.6 + (6.1 x weight (kg)) + (1,023.7 x height (m)) - (9.5 x age). The female model was REE = 1,272.5 + (9.8 x weight (kg)) - (61.6 x height (m)) - (8.2 x age). Our prediction equations showed a nonsignificant difference with REE measured (-3.7 kcal/day) with a significant correlation coefficient (r = 0.67; p prediction equations overestimated and underestimated REE measured. WHO equation developed in normal weight individuals provided the closest values. The two new equations (male and female equations) developed in our study had a good accuracy. Copyright 2006 S. Karger AG, Basel.
Grand, I.; Bellon-Fontaine, M.-N.; Herry, J.-M.; Hilaire, D.; Moriconi, F.-X.; Naïtali, M.
2011-01-01
The standard test methods used to assess the efficiency of a disinfectant applied to surfaces are often based on counting the microbial survivors sampled in a liquid, but total cell removal from surfaces is seldom achieved. One might therefore wonder whether evaluations of microbial survivors in liquid-sampled cells are representative of the levels of survivors in whole populations. The present study was thus designed to determine the “damaged/undamaged” status induced by a peracetic acid disinfection for Bacillus atrophaeus spores deposited on glass coupons directly on this substrate and to compare it to the status of spores collected in liquid by a sampling procedure. The method utilized to assess the viability of both surface-associated and liquid-sampled spores included fluorescence labeling with a combination of Syto 61 and Chemchrome V6 dyes and quantifications by analyzing the images acquired by confocal laser scanning microscopy. The principal result of the study was that the viability of spores sampled in the liquid was found to be poorer than that of surface-associated spores. For example, after 2 min of peracetic acid disinfection, less than 17% ± 5% of viable cells were detected among liquid-sampled cells compared to 79% ± 5% or 47% ± 4%, respectively, when the viability was evaluated on the surface after or without the sampling procedure. Moreover, assessments of the survivors collected in the liquid phase, evaluated using the microscopic method and standard plate counts, were well correlated. Evaluations based on the determination of survivors among the liquid-sampled cells can thus overestimate the efficiency of surface disinfection procedures. PMID:21742922
Grand, I; Bellon-Fontaine, M-N; Herry, J-M; Hilaire, D; Moriconi, F-X; Naïtali, M
2011-09-01
The standard test methods used to assess the efficiency of a disinfectant applied to surfaces are often based on counting the microbial survivors sampled in a liquid, but total cell removal from surfaces is seldom achieved. One might therefore wonder whether evaluations of microbial survivors in liquid-sampled cells are representative of the levels of survivors in whole populations. The present study was thus designed to determine the "damaged/undamaged" status induced by a peracetic acid disinfection for Bacillus atrophaeus spores deposited on glass coupons directly on this substrate and to compare it to the status of spores collected in liquid by a sampling procedure. The method utilized to assess the viability of both surface-associated and liquid-sampled spores included fluorescence labeling with a combination of Syto 61 and Chemchrome V6 dyes and quantifications by analyzing the images acquired by confocal laser scanning microscopy. The principal result of the study was that the viability of spores sampled in the liquid was found to be poorer than that of surface-associated spores. For example, after 2 min of peracetic acid disinfection, less than 17% ± 5% of viable cells were detected among liquid-sampled cells compared to 79% ± 5% or 47% ± 4%, respectively, when the viability was evaluated on the surface after or without the sampling procedure. Moreover, assessments of the survivors collected in the liquid phase, evaluated using the microscopic method and standard plate counts, were well correlated. Evaluations based on the determination of survivors among the liquid-sampled cells can thus overestimate the efficiency of surface disinfection procedures.
Thaller, B.
1992-01-01
This monograph treats most of the usual material to be found in texts on the Dirac equation such as the basic formalism of quantum mechanics, representations of Dirac matrices, covariant realization of the Dirac equation, interpretation of negative energies, Foldy-Wouthuysen transformation, Klein's paradox, spherically symmetric interactions and a treatment of the relativistic hydrogen atom, etc., and also provides excellent additional treatments of a variety of other relevant topics. The monograph contains an extensive treatment of the Lorentz and Poincare groups and their representations. The author discusses in depth Lie algebaic and projective representations, covering groups, and Mackey's theory and Wigner's realization of induced representations. A careful classification of external fields with respect to their behavior under Poincare transformations is supplemented by a basic account of self-adjointness and spectral properties of Dirac operators. A state-of-the-art treatment of relativistic scattering theory based on a time-dependent approach originally due to Enss is presented. An excellent introduction to quantum electrodynamics in external fields is provided. Various appendices containing further details, notes on each chapter commenting on the history involved and referring to original research papers and further developments in the literature, and a bibliography covering all relevant monographs and over 500 articles on the subject, complete this text. This book should satisfy the needs of a wide audience, ranging from graduate students in theoretical physics and mathematics to researchers interested in mathematical physics
Sydoriak, S.G.
1976-01-01
Although criteria for cryostatic stability of superconducting magnets cooled by pool boiling of liquid helium have been widely discussed the same cannot be said for magnets cooled by natural convection or forced flow boiling in channels. Boiling in narrow channels is shown to be qualitatively superior to pool boiling because the recovery heat flux equals the breakaway flux for narrow channels, whereas the two are markedly different in pool boiling. A second advantage of channel boiling is that it is well understood and calculable; pool peak nucleate boiling heat flux has been adequately measured only for boiling from the top of an immersed heated body. Peak boiling from the bottom is much less and (probably) depends strongly on the extent of the bottom surface. Equations are presented by which one can calculate the critical boiling heat flux for parallel wall vertical channels subject to either natural convection or forced flow boiling, with one or both walls heated. The one-heated-wall forced flow equation is discussed with regard to design of a spiral wound solenoid (pancake magnet) having a slippery insulating tape between the windings
Solving Nonlinear Coupled Differential Equations
Mitchell, L.; David, J.
1986-01-01
Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.
Completely integrable operator evolutionary equations
Chudnovsky, D.V.
1979-01-01
The authors present natural generalizations of classical completely integrable equations where the functions are replaced by arbitrary operators. Among these equations are the non-linear Schroedinger, the Korteweg-de Vries, and the modified KdV equations. The Lax representation and the Baecklund transformations are presented. (Auth.)
Kalinowski, M.W.; Szymanowski, L.
1982-03-01
A generalization of the Truesdell F-equations is proposed and some solutions to them - generalized Fox F-functions - are found. It is also shown that a non-linear difference-differential equation, which does not belong to the Truesdell class, nevertheless may be transformed into the standard F-equation. (author)
On the Saha Ionization Equation
Abstract. We revisit the Saha Ionization Equation in order to highlightthe rich interdisciplinary content of the equation thatstraddles distinct areas of spectroscopy, thermodynamics andchemical reactions. In a self-contained discussion, relegatedto an appendix, we delve further into the hidden message ofthe equation in terms ...
Differential equations extended to superspace
Torres, J. [Instituto de Fisica, Universidad de Guanajuato, A.P. E-143, Leon, Guanajuato (Mexico); Rosu, H.C. [Instituto Potosino de Investigacion Cientifica y Tecnologica, A.P. 3-74, Tangamanga, San Luis Potosi (Mexico)
2003-07-01
We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)
Reduction of infinite dimensional equations
Zhongding Li
2006-02-01
Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.
Differential equations extended to superspace
Torres, J.; Rosu, H.C.
2003-01-01
We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)
Taouil Hajer
2012-08-01
Full Text Available This paper is devoted to the helices processes, i.e. the solutions H : ℝ × Ω → ℝd, (t, ω ↦ H(t, ω of the helix equation egin{eqnarray} H(0,o=0; quad H(s+t,o= H(s,Phi(t,o +H(t,oonumber end{eqnarray} H ( 0 ,ω = 0 ; H ( s + t,ω = H ( s, Φ ( t,ω + H ( t,ω where Φ : ℝ × Ω → Ω, (t, ω ↦ Φ(t, ω is a dynamical system on a measurable space (Ω, ℱ. More precisely, we investigate dominated solutions and non differentiable solutions of the helix equation. For the last case, the Wiener helix plays a fundamental role. Moreover, some relations with the cocycle equation defined by Φ, are investigated. Ce papier est consacré aux hélices, c’est-à-dire les solutions H : ℝ × Ω → ℝd, (t, ω ↦ H(t, ω de l’équation fonctionnelle egin{eqnarray} H(0,o=0; quad H(s+t,o= H(s,Phi(t,o +H(t,o onumber end{eqnarray} H ( 0 ,ω = 0 ; H ( s + t,ω = H ( s, Φ ( t,ω + H ( t,ω où Φ : ℝ × Ω → Ω, (t, ω ↦ Φ(t, ω est un système dynamique défini sur un espace mesurable (Ω, ℱ. Plus présisément, nous déterminons d’abord les hélices dominées puis nous caractérisons les hélices non différentiables. Dans ce dernier cas, l’hélice de Wiener joue un rôle important. Nous précisons aussi quelques relations des hélices avec les cocycles définis par Φ.
p-Euler equations and p-Navier-Stokes equations
Li, Lei; Liu, Jian-Guo
2018-04-01
We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.
Generalized quantal equation of motion
Morsy, M.W.; Embaby, M.
1986-07-01
In the present paper, an attempt is made for establishing a generalized equation of motion for quantal objects, in which intrinsic self adjointness is naturally built in, independently of any prescribed representation. This is accomplished by adopting Hamilton's principle of least action, after incorporating, properly, the quantal features and employing the generalized calculus of variations, without being restricted to fixed end points representation. It turns out that our proposed equation of motion is an intrinsically self-adjoint Euler-Lagrange's differential equation that ensures extremization of the quantal action as required by Hamilton's principle. Time dependence is introduced and the corresponding equation of motion is derived, in which intrinsic self adjointness is also achieved. Reducibility of the proposed equation of motion to the conventional Schroedinger equation is examined. The corresponding continuity equation is established, and both of the probability density and the probability current density are identified. (author)
Alternatives to the Dirac equation
Girvin, S.M.; Brownstein, K.R.
1975-01-01
Recent work by Biedenharn, Han, and van Dam (BHvD) has questioned the uniqueness of the Dirac equation. BHvD have obtained a two-component equation as an alternate to the Dirac equation. Although they later show their alternative to be unitarily equivalent to the Dirac equation, certain physical differences were claimed. BHvD attribute the existence of this alternate equation to the fact that their factorizing matrices were position-dependent. To investigate this, we factor the Klein-Gordon equation in spherical coordinates allowing the factorizing matrices to depend arbitrarily upon theta and phi. It is shown that despite this additional freedom, and without involving any relativistic covariance, the conventional four-component Dirac equation is the only possibility
Wave Partial Differential Equation
Szöllös, Alexandr
2009-01-01
Práce se zabývá diferenciálními rovnicemi, jejich využitím při analýze vedení, experimenty s vedením a možnou akcelerací výpočtu v GPU s využitím prostředí nVidia CUDA. This work deals with diffrential equations, with the possibility of using them for analysis of the line and the possibility of accelerating the computations in GPU using nVidia CUDA. C
Gomez, Humberto
2016-06-01
The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm.
Scaling of differential equations
Langtangen, Hans Petter
2016-01-01
The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and exam...
Parabolized stability equations
Herbert, Thorwald
1994-01-01
The parabolized stability equations (PSE) are a new approach to analyze the streamwise evolution of single or interacting Fourier modes in weakly nonparallel flows such as boundary layers. The concept rests on the decomposition of every mode into a slowly varying amplitude function and a wave function with slowly varying wave number. The neglect of the small second derivatives of the slowly varying functions with respect to the streamwise variable leads to an initial boundary-value problem that can be solved by numerical marching procedures. The PSE approach is valid in convectively unstable flows. The equations for a single mode are closely related to those of the traditional eigenvalue problems for linear stability analysis. However, the PSE approach does not exploit the homogeneity of the problem and, therefore, can be utilized to analyze forced modes and the nonlinear growth and interaction of an initial disturbance field. In contrast to the traditional patching of local solutions, the PSE provide the spatial evolution of modes with proper account for their history. The PSE approach allows studies of secondary instabilities without the constraints of the Floquet analysis and reproduces the established experimental, theoretical, and computational benchmark results on transition up to the breakdown stage. The method matches or exceeds the demonstrated capabilities of current spatial Navier-Stokes solvers at a small fraction of their computational cost. Recent applications include studies on localized or distributed receptivity and prediction of transition in model environments for realistic engineering problems. This report describes the basis, intricacies, and some applications of the PSE methodology.
Pomeau, Yves; Piasecki, Jarosław
2017-11-01
The existence of atoms has been long predicted by philosophers and scientists. The development of thermodynamics and of the statistical interpretation of its concepts at the end of the nineteenth century and in the early years of the twentieth century made it possible to bridge the gap of scales between the macroscopic world and the world of atoms. Einstein and Smoluchowski showed in 1905 and 1906 that the Brownian motion of particles of measurable size is a manifestation of the motion of atoms in fluids. Their derivation was completely different from each other. Langevin showed in 1908 how to put in a coherent framework the subtle effect of the randomness of the atomic world, responsible for the fluctuating force driving the motion of the Brownian particle and the viscosity of the "macroscopic" flow taking place around the same Brownian particle. Whereas viscous forces were already well understood at this time, the "Langevin" force appears there for the first time: it represents the fluctuating part of the interaction between the Brownian particle and the surrounding fluid. We discuss the derivation by Einstein and Smoluchowski as well as a previous paper by Sutherland on the diffusion coefficient of large spheres. Next we present Langevin's short note and explain the fundamental splitting into a random force and a macroscopic viscous force. This brings us to discuss various points, like the kind of constraints on Langevin-like equations. We insist in particular on the one arising from the time-reversal symmetry of the equilibrium fluctuations. Moreover, we discuss another constraint, raised first by Lorentz, which implies that, if the Brownian particle is not very heavy, the viscous force cannot be taken as the standard Stokes drag on an object moving at uniform speed. Lastly, we examine the so-called Langevin-Heisenberg and/or Langevin-Schrödinger equation used in quantum mechanics.
Modeling a Predictive Energy Equation Specific for Maintenance Hemodialysis.
Byham-Gray, Laura D; Parrott, J Scott; Peters, Emily N; Fogerite, Susan Gould; Hand, Rosa K; Ahrens, Sean; Marcus, Andrea Fleisch; Fiutem, Justin J
2017-03-01
Hypermetabolism is theorized in patients diagnosed with chronic kidney disease who are receiving maintenance hemodialysis (MHD). We aimed to distinguish key disease-specific determinants of resting energy expenditure to create a predictive energy equation that more precisely establishes energy needs with the intent of preventing protein-energy wasting. For this 3-year multisite cross-sectional study (N = 116), eligible participants were diagnosed with chronic kidney disease and were receiving MHD for at least 3 months. Predictors for the model included weight, sex, age, C-reactive protein (CRP), glycosylated hemoglobin, and serum creatinine. The outcome variable was measured resting energy expenditure (mREE). Regression modeling was used to generate predictive formulas and Bland-Altman analyses to evaluate accuracy. The majority were male (60.3%), black (81.0%), and non-Hispanic (76.7%), and 23% were ≥65 years old. After screening for multicollinearity, the best predictive model of mREE ( R 2 = 0.67) included weight, age, sex, and CRP. Two alternative models with acceptable predictability ( R 2 = 0.66) were derived with glycosylated hemoglobin or serum creatinine. Based on Bland-Altman analyses, the maintenance hemodialysis equation that included CRP had the best precision, with the highest proportion of participants' predicted energy expenditure classified as accurate (61.2%) and with the lowest number of individuals with underestimation or overestimation. This study confirms disease-specific factors as key determinants of mREE in patients on MHD and provides a preliminary predictive energy equation. Further prospective research is necessary to test the reliability and validity of this equation across diverse populations of patients who are receiving MHD.
Merghani, Tarig H; Alawad, Azza O; Ibrahim, Rihab M; Abdelmoniem, Asim M
2015-08-15
Few studies investigated the association between basal metabolic rate (BMR) and indicators of pulmonary function. This study was conducted to estimate BMR in overweight/obese and non-obese healthy subjects using four commonly used predictive equations and to investigate its relation to the indicators of lung function tests (LFT). A cross sectional study was conducted in Tabuk University, Tabuk, Saudi Arabia. A total of 201 students (98 males and 103 females) participated in the study. Four different values of BMR were calculated for each participant using four different predictive equations (Harris-Benedict, Mifflin, FAO/WHO/UNU and Henry-Rees). A portable All-flow spirometer (Clement Clarke International, Harlow, UK) was used for measurements of LFT. Significantly higher values of spirometric indicators (p BMR values predicted with the four equations were significantly higher in the males compared to the females and among the overweight/obese compared to the non-obese subjects (p BMR values and the indicators of LFT was statistically insignificant (p > 0.05). Mean values of LFT indicators are not related to the estimated values of BMR. A practical calculation of BMR based on direct measurement of oxygen consumption is recommended to confirm the absence of this association.
Ichihara, Noriko; Namba, Kazuyoshi; Ishikawa-Takata, Kazuko; Sekine, Kazunori; Takase, Mitsunori; Kamada, Yuko; Fujii, Seigo
2012-10-01
This study aimed to clarify the energy requirement in patients with amyotrophic lateral sclerosis (ALS) undergoing tracheostomy positive pressure ventilation with tracheostomy. Total energy expenditure (TEE) was measured in 10 hospitalized bedridden ALS patients using the doubly-labeled water (DLW) method. The mean TEE/day and TEE/fat- free mass estimated by DLW method were 934 ± 201 kcal/day and 34.8 ± 5.5 kcal/kg/day, respectively. The mean TEE/resting metabolic rate (RMR) was 0.85 when RMR was estimated by the Harris-Benedict equation, 0.91 by Dietary Reference Intake (DRI), and 0.97 by Ganpule's equation using fat-free mass (FFM). The ratios of TEE to measured RMR were 1.05, 1.15 and 1.23 in three patients. In conclusion, multiplying measured RMR by 1.1 to 1.2 is considered to be appropriate to estimate energy need. However, because it is difficult to measure RMR directly in a clinical setting, an appropriate equation for estimating RMR for ALS patient should be developed.
Introduction to partial differential equations
Borthwick, David
2016-01-01
This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions: (1) What is the scientific problem we are trying to understand? (2) How do we model that with PDE? (3) What techniques can we use to analyze the PDE? (4) How do those techniques apply to this equation? (5) What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.
Analytic solutions of hydrodynamics equations
Coggeshall, S.V.
1991-01-01
Many similarity solutions have been found for the equations of one-dimensional (1-D) hydrodynamics. These special combinations of variables allow the partial differential equations to be reduced to ordinary differential equations, which must then be solved to determine the physical solutions. Usually, these reduced ordinary differential equations are solved numerically. In some cases it is possible to solve these reduced equations analytically to obtain explicit solutions. In this work a collection of analytic solutions of the 1-D hydrodynamics equations is presented. These can be used for a variety of purposes, including (i) numerical benchmark problems, (ii) as a basis for analytic models, and (iii) to provide insight into more complicated solutions
On matrix fractional differential equations
Adem Kılıçman
2017-01-01
Full Text Available The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.
Differential equations methods and applications
Said-Houari, Belkacem
2015-01-01
This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory. To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included. The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. .
Integral equations and their applications
Rahman, M
2007-01-01
For many years, the subject of functional equations has held a prominent place in the attention of mathematicians. In more recent years this attention has been directed to a particular kind of functional equation, an integral equation, wherein the unknown function occurs under the integral sign. The study of this kind of equation is sometimes referred to as the inversion of a definite integral. While scientists and engineers can already choose from a number of books on integral equations, this new book encompasses recent developments including some preliminary backgrounds of formulations of integral equations governing the physical situation of the problems. It also contains elegant analytical and numerical methods, and an important topic of the variational principles. Primarily intended for senior undergraduate students and first year postgraduate students of engineering and science courses, students of mathematical and physical sciences will also find many sections of direct relevance. The book contains eig...
Stochastic partial differential equations
Lototsky, Sergey V
2017-01-01
Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected ...
Menikoff, Ralph [Los Alamos National Laboratory
2015-12-15
The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ≥ 0, T ≥ 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.
Wetterich, C.
2018-06-01
We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.
The generalized Airy diffusion equation
Frank M. Cholewinski
2003-08-01
Full Text Available Solutions of a generalized Airy diffusion equation and an associated nonlinear partial differential equation are obtained. Trigonometric type functions are derived for a third order generalized radial Euler type operator. An associated complex variable theory and generalized Cauchy-Euler equations are obtained. Further, it is shown that the Airy expansions can be mapped onto the Bessel Calculus of Bochner, Cholewinski and Haimo.
Supersymmetric two-particle equations
Sissakyan, A.N.; Skachkov, N.B.; Shevchenko, O.Yu.
1986-01-01
In the framework of the scalar superfield model, a particular case of which is the well-known Wess-Zumino model, the supersymmetric Schwinger equations are found. On their basis with the use of the second Legendre transformation the two-particle supersymmetric Edwards and Bethe-Salpeter equations are derived. A connection of the kernels and inhomogeneous terms of these equations with generating functional of the second Legendre transformation is found
Introduction to ordinary differential equations
Rabenstein, Albert L
1966-01-01
Introduction to Ordinary Differential Equations is a 12-chapter text that describes useful elementary methods of finding solutions using ordinary differential equations. This book starts with an introduction to the properties and complex variable of linear differential equations. Considerable chapters covered topics that are of particular interest in applications, including Laplace transforms, eigenvalue problems, special functions, Fourier series, and boundary-value problems of mathematical physics. Other chapters are devoted to some topics that are not directly concerned with finding solutio
On matrix fractional differential equations
Adem Kılıçman; Wasan Ajeel Ahmood
2017-01-01
The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objec...
Electronic representation of wave equation
Veigend, Petr; Kunovský, Jiří, E-mail: kunovsky@fit.vutbr.cz; Kocina, Filip; Nečasová, Gabriela; Valenta, Václav [University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic); Šátek, Václav [IT4Innovations, VŠB Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava-Poruba (Czech Republic); University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic)
2016-06-08
The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.
Generalized Lorentz-Force equations
Yamaleev, R.M.
2001-01-01
Guided by Nambu (n+1)-dimensional phase space formalism we build a new system of dynamic equations. These equations describe a dynamic state of the corporeal system composed of n subsystems. The dynamic equations are formulated in terms of dynamic variables of the subsystems as well as in terms of dynamic variables of the corporeal system. These two sets of variables are related respectively as roots and coefficients of the n-degree polynomial equation. In the special n=2 case, this formalism reproduces relativistic dynamics for the charged spinning particles
The forced nonlinear Schroedinger equation
Kaup, D.J.; Hansen, P.J.
1985-01-01
The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)
Correct Linearization of Einstein's Equations
Rabounski D.
2006-06-01
Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.
The Dirac equation for accountants
Ord, G.N.
2006-01-01
In the context of relativistic quantum mechanics, derivations of the Dirac equation usually take the form of plausibility arguments based on experience with the Schroedinger equation. The primary reason for this is that we do not know what wavefunctions physically represent, so derivations have to rely on formal arguments. There is however a context in which the Dirac equation in one dimension is directly related to a classical generating function. In that context, the derivation of the Dirac equation is an exercise in counting. We provide this derivation here and discuss its relationship to quantum mechanics
Difference equations theory, applications and advanced topics
Mickens, Ronald E
2015-01-01
THE DIFFERENCE CALCULUS GENESIS OF DIFFERENCE EQUATIONS DEFINITIONS DERIVATION OF DIFFERENCE EQUATIONS EXISTENCE AND UNIQUENESS THEOREM OPERATORS ∆ AND E ELEMENTARY DIFFERENCE OPERATORS FACTORIAL POLYNOMIALS OPERATOR ∆−1 AND THE SUM CALCULUS FIRST-ORDER DIFFERENCE EQUATIONS INTRODUCTION GENERAL LINEAR EQUATION CONTINUED FRACTIONS A GENERAL FIRST-ORDER EQUATION: GEOMETRICAL METHODS A GENERAL FIRST-ORDER EQUATION: EXPANSION TECHNIQUES LINEAR DIFFERENCE EQUATIONSINTRODUCTION LINEARLY INDEPENDENT FUNCTIONS FUNDAMENTAL THEOREMS FOR HOMOGENEOUS EQUATIONSINHOMOGENEOUS EQUATIONS SECOND-ORDER EQUATIONS STURM-LIOUVILLE DIFFERENCE EQUATIONS LINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS CONSTRUCTION OF A DIFFERENCE EQUATION HAVING SPECIFIED SOLUTIONS RELATIONSHIP BETWEEN LINEAR DIFFERENCE AND DIFFERENTIAL EQUATIONS INHOMOGENEOUS EQUATIONS: METHOD OF UNDETERMINED COEFFICIENTS INHOMOGENEOUS EQUATIONS: OPERATOR METHODS z-TRANSFORM METHOD SYSTEMS OF DIFFERENCE EQUATIONS LINEAR PARTIAL DIFFERENCE EQUATI...
Differential equations a dynamical systems approach ordinary differential equations
Hubbard, John H
1991-01-01
This is a corrected third printing of the first part of the text Differential Equations: A Dynamical Systems Approach written by John Hubbard and Beverly West. The authors' main emphasis in this book is on ordinary differential equations. The book is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. Traditional courses on differential equations focus on techniques leading to solutions. Yet most differential equations do not admit solutions which can be written in elementary terms. The authors have taken the view that a differential equations defines functions; the object of the theory is to understand the behavior of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods. The companion software, MacMath, is designed to bring these notions to life.
Srivastava, Richa; Batra, Atul; Dhawan, Deepa; Bakhshi, Sameer
2017-02-01
Increased obesity in leukemia survivors has been attributed to chemotherapy and radiation. Data on total energy intake (TEI) and total energy expenditure (TEE) are lacking in obese childhood leukemia patients after completion of therapy from India. We conducted a cross-sectional study in pediatric acute leukemia patients after completion of therapy wherein energy intake was assessed by 24-hour recall method. TEE was calculated using Harris-Benedict equation, by assessing the physical activity level using Physical Activity Questionnaire for children and basal metabolic rate by World Health Organization equation. Indian Academy of Pediatrics 2015 guidelines for BMI were used for defining overweight and obesity. Nutritional status was assessed in 150 leukemia patients after completion of therapy. Twenty-five percent of leukemia patients after completion of therapy were overweight and obese versus 11% of healthy controls (p = 0.042). The mean ratio of TEI/required energy intake (REI), TEE/required energy expenditure (REE), and (TEI:REI)/(TEE:REE) were significantly higher in overweight and obese group versus nonobese survivors (p obesity. Obesity in leukemia patients after completion of therapy is associated with increased energy intake, causing imbalance between energy intake and TEE in these patients.
Solutions to Arithmetic Convolution Equations
Glöckner, H.; Lucht, L.G.; Porubský, Štefan
2007-01-01
Roč. 135, č. 6 (2007), s. 1619-1629 ISSN 0002-9939 R&D Projects: GA ČR GA201/04/0381 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic functions * Dirichlet convolution * polynomial equations * analytic equations * topological algebras * holomorphic functional calculus Subject RIV: BA - General Mathematics Impact factor: 0.520, year: 2007
On Degenerate Partial Differential Equations
Chen, Gui-Qiang G.
2010-01-01
Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial differential equations, are presented, which arise naturally in some longstanding, fundamental problems in fluid mechanics and differential geometry. The solution to these fundamental problems greatly requires a deep understanding of nonlinear degenerate parti...
Differential equations a concise course
Bear, H S
2011-01-01
Concise introduction for undergraduates includes, among other topics, a survey of first order equations, discussions of complex-valued solutions, linear differential operators, inverse operators and variation of parameters method, the Laplace transform, Picard's existence theorem, and an exploration of various interpretations of systems of equations. Numerous clearly stated theorems and proofs, examples, and problems followed by solutions.
Differential equations and finite groups
Put, Marius van der; Ulmer, Felix
2000-01-01
The classical solution of the Riemann-Hilbert problem attaches to a given representation of the fundamental group a regular singular linear differential equation. We present a method to compute this differential equation in the case of a representation with finite image. The approach uses Galois
Saturation and linear transport equation
Kutak, K.
2009-03-01
We show that the GBW saturation model provides an exact solution to the one dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting term in the diffusive approximation are balanced by the nonlinear term. (orig.)
Lie symmetries in differential equations
Pleitez, V.
1979-01-01
A study of ordinary and Partial Differential equations using the symmetries of Lie groups is made. Following such a study, an application to the Helmholtz, Line-Gordon, Korleweg-de Vries, Burguer, Benjamin-Bona-Mahony and wave equations is carried out [pt
Introduction to nonlinear dispersive equations
Linares, Felipe
2015-01-01
This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...
Students' Understanding of Quadratic Equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-01-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…
Solving equations by topological methods
Lech Górniewicz
2005-01-01
Full Text Available In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations.
Generalized Fermat equations: A miscellany
Bennett, M.A.; Chen, I.; Dahmen, S.R.; Yazdani, S.
2015-01-01
This paper is devoted to the generalized Fermat equation xp + yq = zr, where p, q and r are integers, and x, y and z are nonzero coprime integers. We begin by surveying the exponent triples (p, q, r), including a number of infinite families, for which the equation has been solved to date, detailing
Equation with the many fathers
Kragh, Helge
1984-01-01
In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the us...... as electrodynamics. Although this ambitious attempt attracted some interest in 1926, its impact on the mainstream of development in quantum mechanics was virtually nil....... of the usual Schrödinger equation. In most of the early versions the Klein-Gordon equation was connected with the general theory of relativity. Klein and some other physicists attempted to express quantum mechanics within a five-dimensional unified theory, embracing general relativity as well...
The relativistic electron wave equation
Dirac, P.A.M.
1977-08-01
The paper was presented at the European Conference on Particle Physics held in Budapest between the 4th and 9th July of 1977. A short review is given on the birth of the relativistic electron wave equation. After Schroedinger has shown the equivalence of his wave mechanics and the matrix mechanics of Heisenberg, a general transformation theory was developed by the author. This theory required a relativistic wave equation linear in delta/delta t. As the Klein--Gordon equation available at this time did not satisfy this condition the development of a new equation became necessary. The equation which was found gave the value of the electron spin and magnetic moment automatically. (D.P.)
Higher order field equations. II
Tolhoek, H.A.
1977-01-01
In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for mod(M)→infinity the Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) approach the Green's functions Δsub(R)(x) and Δsub(A)(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) is the same as of Δsub(R)(x) and Δsub(A)(x)-and also the same as for Dsub(R)(x) and Dsub(A)(x) for t→+-infinity;, where Dsub(R) and Dsub(A) are the Green's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense. (Auth.)
Choudhary, M.R.; Mustafa, U.S.
2009-01-01
Field tests were conducted to calibrate the existing SCS design equation in determining field border length using field data of different field lengths during 2nd and 3rd irrigations under local conditions. A single ring infiltrometer was used to estimate the water movement into and through the irrigated soil profile and in estimating the coefficients of Kostiakov infiltration function. Measurements of the unit discharge and time of advance were carried out during different irrigations on wheat irrigated fields having clay loam soil. The collected field data were used to calibrate the existing SCS design equation developed by USDA for testing its validity under local field conditions. SCS equation was modified further to improve its applicability. Results from the study revealed that the Kostiakov model over predicted the coefficients, which in turn overestimated the water advance length for boarder in the selected field using existing SCS design equation. However, the calibrated SCS design equation after parametric modification produced more satisfactory results encouraging the scientists to make its use at larger scale. (author)
Ozdemir, Burhanettin
2017-01-01
The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…
Validity of a population-specific BMR predictive equation for adults from an urban tropical setting.
Wahrlich, Vivian; Teixeira, Tatiana Miliante; Anjos, Luiz Antonio Dos
2018-02-01
Basal metabolic rate (BMR) is an important physiologic measure in nutrition research. In many instances it is not measured but estimated by predictive equations. The purpose of this study was to compare measured BMR (BMRm) with estimated BMR (BMRe) obtained by different equations. A convenient sample of 148 (89 women) 20-60 year-old subjects from the metropolitan area of Rio de Janeiro, Brazil participated in the study. BMRm values were measured by an indirect calorimeter and predicted by different equations (Schofield, Henry and Rees, Mifflin-St. Jeor and Anjos. All subjects had their body composition and anthropometric variables also measured. Accuracy of the estimations was established by the percentage of BMRe falling within ±10% of BMRm and bias when the 95% CI of the difference of BMRe and BMRm means did not include zero. Mean BMRm values were 4833.5 (SD 583.3) and 6278.8 (SD 724.0) kJ*day -1 for women and men, respectively. BMRe values were both biased and inaccurate except for values predicted by the Anjos equation. BMR overestimation was approximately 20% for the Schofield equation which was higher comparatively to the Henry and Rees (14.5% and 9.6% for women and men, respectively) and the Mifflin-St. Jeor (approximately 14.0%) equations. BMR estimated by the Anjos equation was unbiased (95% CI = -78.1; 96.3 kJ day -1 for women and -282.6; 30.7 kJ*day -1 for men). Population-specific BMR predictive equations yield unbiased and accurate BMR values in adults from an urban tropical setting. Copyright © 2016 Elsevier Ltd and European Society for Clinical Nutrition and Metabolism. All rights reserved.
Neoclassical MHD equations for tokamaks
Callen, J.D.; Shaing, K.C.
1986-03-01
The moment equation approach to neoclassical-type processes is used to derive the flows, currents and resistive MHD-like equations for studying equilibria and instabilities in axisymmetric tokamak plasmas operating in the banana-plateau collisionality regime (ν* approx. 1). The resultant ''neoclassical MHD'' equations differ from the usual reduced equations of resistive MHD primarily by the addition of the important viscous relaxation effects within a magnetic flux surface. The primary effects of the parallel (poloidal) viscous relaxation are: (1) Rapid (approx. ν/sub i/) damping of the poloidal ion flow so the residual flow is only toroidal; (2) addition of the bootstrap current contribution to Ohm's laws; and (3) an enhanced (by B 2 /B/sub theta/ 2 ) polarization drift type term and consequent enhancement of the perpendicular dielectric constant due to parallel flow inertia, which causes the equations to depend only on the poloidal magnetic field B/sub theta/. Gyroviscosity (or diamagnetic vfiscosity) effects are included to properly treat the diamagnetic flow effects. The nonlinear form of the neoclassical MHD equations is derived and shown to satisfy an energy conservation equation with dissipation arising from Joule and poloidal viscous heating, and transport due to classical and neoclassical diffusion
Approximate solutions to Mathieu's equation
Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.
2018-06-01
Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.
Soliton equations and Hamiltonian systems
Dickey, L A
2002-01-01
The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau
Galois theory of difference equations
Put, Marius
1997-01-01
This book lays the algebraic foundations of a Galois theory of linear difference equations and shows its relationship to the analytic problem of finding meromorphic functions asymptotic to formal solutions of difference equations. Classically, this latter question was attacked by Birkhoff and Tritzinsky and the present work corrects and greatly generalizes their contributions. In addition results are presented concerning the inverse problem in Galois theory, effective computation of Galois groups, algebraic properties of sequences, phenomena in positive characteristics, and q-difference equations. The book is aimed at advanced graduate researchers and researchers.
Integral equation methods for electromagnetics
Volakis, John
2012-01-01
This text/reference is a detailed look at the development and use of integral equation methods for electromagnetic analysis, specifically for antennas and radar scattering. Developers and practitioners will appreciate the broad-based approach to understanding and utilizing integral equation methods and the unique coverage of historical developments that led to the current state-of-the-art. In contrast to existing books, Integral Equation Methods for Electromagnetics lays the groundwork in the initial chapters so students and basic users can solve simple problems and work their way up to the mo
Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation
Wang, D.
2017-12-01
The empirical Budyko equation represents the partitioning of mean annual precipitation into evaporation and runoff. Richards' equation, based on Darcy's law, represents the movement of water in unsaturated soils. The linkage between Richards' equation and Budyko equation is presented by invoking the empirical Soil Conservation Service curve number (SCS-CN) model for computing surface runoff at the event-scale. The basis of the SCS-CN method is the proportionality relationship, i.e., the ratio of continuing abstraction to its potential is equal to the ratio of surface runoff to its potential value. The proportionality relationship can be derived from the Richards' equation for computing infiltration excess and saturation excess models at the catchment scale. Meanwhile, the generalized proportionality relationship is demonstrated as the common basis of SCS-CN method, monthly "abcd" model, and Budyko equation. Therefore, the linkage between Darcy's law and the emergent pattern of mean annual water balance at the catchment scale is presented through the proportionality relationship.
Iterative Splitting Methods for Differential Equations
Geiser, Juergen
2011-01-01
Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential
Nonlinear integrodifferential equations as discrete systems
Tamizhmani, K. M.; Satsuma, J.; Grammaticos, B.; Ramani, A.
1999-06-01
We analyse a class of integrodifferential equations of the `intermediate long wave' (ILW) type. We show that these equations can be formally interpreted as discrete, differential-difference systems. This allows us to link equations of this type with previous results of ours involving differential-delay equations and, on the basis of this, propose new integrable equations of ILW type. Finally, we extend this approach to pure difference equations and propose ILW forms for the discrete lattice KdV equation.
Direct 'delay' reductions of the Toda equation
Joshi, Nalini
2009-01-01
A new direct method of obtaining reductions of the Toda equation is described. We find a canonical and complete class of all possible reductions under certain assumptions. The resulting equations are ordinary differential-difference equations, sometimes referred to as delay-differential equations. The representative equation of this class is hypothesized to be a new version of one of the classical Painleve equations. The Lax pair associated with this equation is obtained, also by reduction. (fast track communication)
Energy metabolism and nutritional status in hospitalized patients with lung cancer.
Takemura, Yumi; Sasaki, Masaya; Goto, Kenichi; Takaoka, Azusa; Ohi, Akiko; Kurihara, Mika; Nakanishi, Naoko; Nakano, Yasutaka; Hanaoka, Jun
2016-09-01
This study aimed to investigate the energy metabolism of patients with lung cancer and the relationship between energy metabolism and proinflammatory cytokines. Twenty-eight patients with lung cancer and 18 healthy controls were enrolled in this study. The nutritional status upon admission was analyzed using nutritional screening tools and laboratory tests. The resting energy expenditure and respiratory quotient were measured using indirect calorimetry, and the predicted resting energy expenditure was calculated using the Harris-Benedict equation. Energy expenditure was increased in patients with advanced stage disease, and there were positive correlations between measured resting energy expenditure/body weight and interleukin-6 levels and between measured resting energy expenditure/predicted resting energy expenditure and interleukin-6 levels. There were significant relationships between body mass index and plasma leptin or acylated ghrelin levels. However, the level of appetite controlling hormones did not affect dietary intake. There was a negative correlation between plasma interleukin-6 levels and dietary intake, suggesting that interleukin-6 plays a role in reducing dietary intake. These results indicate that energy expenditure changes significantly with lung cancer stage and that plasma interleukin-6 levels affect energy metabolism and dietary intake. Thus, nutritional management that considers the changes in energy metabolism is important in patients with lung cancer.
Serum carnitine levels in bone marrow transplant recipients.
Kirvelä, O; Antila, H; Heinonen, O; Toivanen, A
1990-12-01
This study investigated plasma carnitine levels in patients undergoing allogenic bone marrow transplantation. The patients received fat-based TPN (50% fat, 50% CHO; calorie: nitrogen ratio 125:1) for an average of 33 +/- 7.5 days. TPN was started before transplantation and stopped when patients were able to eat. Caloric needs were estimated using the Harris-Benedict equation; 150% of the estimated BEE was given for the first two weeks after transplantation. The amount of TPN was gradually decreased as patients resumed their oral intake. All patients had low-normal serum carnitine levels before transplantation. There was no significant change in total or free serum carnitine levels during the course of TPN. However, in patients who had symptoms of graft vs. host reaction (GVH), the highest carnitine values during GVH (total 72.3 +/- 6.5 and free 61.2 +/- 12.4 mumol/l) were significantly higher (p < 0.001) than the baseline values (total 27.1 +/- 9.3 and free 24.9 +/- 9.6 mumol/l) or the highest non GVH values after transplantation (total 32.0 +/- 10.7 and free 29.0 +/- 10.7 mumol/l, respectively). The serum triglyceride, total cholesterol, and HDL cholesterol remained within normal range. In conclusion, bone marrow transplant patients receiving fat-based TPN have normal circulating levels of carnitine. GVH reaction caused an increase in the carnitine levels, which was probably due to increased tissue catabolism.
Nishiwaki, Satoshi; Miyamura, Koichi; Seto, Aika; Watanabe, Keisuke; Yanagisawa, Mayumi; Imahashi, Nobuhiko; Shimba, Makoto; Yasuda, Takahiko; Kuwatsuka, Yachiyo; Oba, Taku; Terakura, Seitaro; Kodera, Yoshihisa
2009-09-01
Early deaths after allogeneic stem cell transplantation (allo-SCT) are of major concern. On the assumption that both decreased and increased basal metabolism might relate to early deaths, we analyzed the risk factors for overall survival to days 30 (OS30) and 60 (OS60). The Harris-Benedict equation was used to calculate basal metabolism. Comparing a patient's basal metabolism (PBM) calculated from pretransplant body weight with the standard basal metabolism (SBM) calculated from standard body weight (body mass index (BMI) = 22), we defined the basal metabolic ratio (BMR) as a parameter (BMR = PBM/SBM). We retrospectively analyzed 360 adult patients transplanted between 1997 and 2006 at a single center in Japan. A multivariate analysis of OS30 showed risk factors to be: BMR BMR; LBR) (P = 0.01), BMR > 1.05 (high BMR; HBR) (P = 0.005) and non-complete remission (non-CR) (P 5 0.001), whereas a multivariate analysis of OS60 showed those risk factors to be: LBR (P = 0.02), HBR (P = 0.04), non-CR (P = 0.002), and performance status BMR BMR; ABR) (96.8 and 90.3% for ABR, 87.1 and 76.2% for LBR, and 87.8 and 81.1% for HBR). In conclusion, BMR could prove to be a predictor of early death after allo-SCT.
[Nutritional support in sepsis].
Ortiz Leyba, C; López Martínez, J; Blesa Malpica, A L
2005-06-01
Although it is considered that metabolic and nutritional support must be part of the management of septic patients, it has not been conclusively shown that nutritional support will improve survival or complications from sepsis. Specific data on this issue are scarce since there are few studies that have investigated specialized nutritional support in septic patients. Thus, most of the recommendations are based on outcomes obtained in severely ill patients with different pathologies. It is assumed that nutritional support should be carried out through the enteral route whenever possible, as in other critically ill patients. The energetic waste in these patients is highly variable, although in general terms the hypermetabolic situation may be classified as moderate. An adjustment factor of 1.25-1.30 is recommended for the Harris-Benedict's equation to calculate the caloric intake. Septic patients should receive a hyperproteic intake. The amount of glucose administered should not exceed 70% of non-protein calories, and lipids intake should not exceed 40%. With regards to micronutrients, it is recommended to increase the supply of those with antioxidant properties (vitamin E, carotenes, vitamin C, selenium). There are data to consider that the use of diets enriched with pharmaco-nutrients (both with parenteral and enteral routes) may be beneficial in septic patients, although there is some controversy when interpreting the outcomes.
Mohan, A; Poulose, R; Kulshreshtha, I; Chautani, A M; Madan, K; Hadda, V; Guleria, R
2017-07-01
The relation between dietary intake and metabolic profile in non-small cell lung cancer (NSCLC) was evaluated. Patients with NSCLC were recruited and their caloric requirement and resting energy expenditure (REE) were calculated using the Harris-Benedict equation and Katch-McArdle formula respectively. Hypermetabolic state was defined as REE more than 10% above the basal metabolic rate (BMR). Body composition parameters were calculated by bioelectric impedance method. The 24-h dietary intake method and Malnutrition Universal Screening Tool assessed nutritional intake. One hundred and forty-eight subjects were included (87% males). Of these, 46.6% subjects were hypermetabolic and 31% cachexic, with lower calorie and protein intakes than recommended, although per cent of total energy derived from protein, fat and carbohydrates were similar. Hypermetabolic patients had lower BMI, though the per cent deficit in energy and protein consumption was similar. Cachexia was associated with lower BMR but not with deficit in energy or protein consumption. No correlation was seen between dietary intake and body composition parameters. The calorie and protein intake of NSCLC patients is lower than recommended. The discordance between elevated REE and dietary intake implies that the relationship between increased energy demands and food intake may be altered. © 2016 John Wiley & Sons Ltd.
Noninvasive ventilation reduces energy expenditure in amyotrophic lateral sclerosis.
Georges, Marjolaine; Morélot-Panzini, Capucine; Similowski, Thomas; Gonzalez-Bermejo, Jesus
2014-02-07
Amyotrophic lateral sclerosis (ALS) leads to chronic respiratory failure. Diaphragmatic dysfunction, a major driver of dyspnea and mortality, is associated with a shift of the burden of ventilation to extradiaphragmatic inspiratory muscles, including neck muscles. Besides, energy expenditure is often abnormally high in ALS, and this is associated with a negative prognostic value. We hypothesized that noninvasive ventilation (NIV) would relieve inspiratory neck muscles and reduce resting energy expenditure (REE). Using indirect calorimetry, we measured REE during spontaneous breathing (REESB) and NIV (REENIV) in 16 ALS patients with diaphragmatic dysfunction, during the first 3 months of NIV. Measured values were compared with predicted REE (REEpred)(Harris-Benedict equation). NIV abolished inspiratory neck muscle activity. Even though our patients were not hypermetabolic, on the contrary, with a REESB that was lower than REEpred (average 11%), NIV did reduce energy expenditure. Indeed, median REENIV, in this population with a mean body mass index of 21.4 kg.m-2, was 1149 kcal/24 h [interquartile 970-1309], lower than REESB (1197 kcal/24 h, 1054-1402; mean difference 7%; p = 0.03, Wilcoxon). REESB and REENIV were correlated with forced vital capacity and maximal inspiratory pressure. NIV can reduce energy expenditure in ALS patients probably by alleviating the ventilatory burden imposed on inspiratory neck muscles to compensate diaphragm weakness. It remains to be elucidated whether or not, in which population, and to what extent, NIV can be beneficial in ALS through the corresponding reduction in energy expenditure.
Integral equation for Coulomb problem
Sasakawa, T.
1986-01-01
For short range potentials an inhomogeneous (homogeneous) Lippmann-Schwinger integral equation of the Fredholm type yields the wave function of scattering (bound) state. For the Coulomb potential, this statement is no more valid. It has been felt difficult to express the Coulomb wave function in a form of an integral equation with the Coulomb potential as the perturbation. In the present paper, the author shows that an inhomogeneous integral equation of a Volterra type with the Coulomb potential as the perturbation can be constructed both for the scattering and the bound states. The equation yielding the binding energy is given in an integral form. The present treatment is easily extended to the coupled Coulomb problems
Geophysical interpretation using integral equations
Eskola, L
1992-01-01
Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu med to have a back...
Singularity: Raychaudhuri equation once again
Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quan- tum gravity ... than the observation verifying the prediction of theory. This gave .... which was now expanding, would have had a singular beginning in a hot Big Bang.
Kinetic equations in dirty superconductors
Kraehenbuehl, Y.
1981-01-01
Kinetic equations for superconductors in the dirty limit are derived using a method developed for superfluid systems, which allows a systematic expansion in small parameters; exact charge conservation is obeyed. (orig.)
Skyrme, T.H.R.
1994-01-01
In a model quantum theory of interacting mesons, the motion of certain conserved particle-like structures is discussed. It is shown how collective coordinates may be introduced to describe them, leading, in lowest approximation, to a Dirac equation. (author)
Solving Differential Equations in R
Although R is still predominantly applied for statistical analysis and graphical representation, it is rapidly becoming more suitable for mathematical computing. One of the fields where considerable progress has been made recently is the solution of differential equations. Here w...
Wave-equation dispersion inversion
Li, Jing; Feng, Zongcai; Schuster, Gerard T.
2016-01-01
We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained
Jannussis, A.; Streclas, A.; Sourlas, D.; Vlachos, K.
1977-01-01
Using the theorem of the derivative of a function of operators with respect to any parameter, we can find the equation of motion of a system in classical mechanics, in canonical as well as in non-canonical mechanics
Quantum-statistical kinetic equations
Loss, D.; Schoeller, H.
1989-01-01
Considering a homogeneous normal quantum fluid consisting of identical interacting fermions or bosons, the authors derive an exact quantum-statistical generalized kinetic equation with a collision operator given as explicit cluster series where exchange effects are included through renormalized Liouville operators. This new result is obtained by applying a recently developed superoperator formalism (Liouville operators, cluster expansions, symmetrized projectors, P q -rule, etc.) to nonequilibrium systems described by a density operator ρ(t) which obeys the von Neumann equation. By means of this formalism a factorization theorem is proven (being essential for obtaining closed equations), and partial resummations (leading to renormalized quantities) are performed. As an illustrative application, the quantum-statistical versions (including exchange effects due to Fermi-Dirac or Bose-Einstein statistics) of the homogeneous Boltzmann (binary collisions) and Choh-Uhlenbeck (triple collisions) equations are derived
Lorentz Covariance of Langevin Equation
Koide, T.; Denicol, G.S.; Kodama, T.
2008-01-01
Relativistic covariance of a Langevin type equation is discussed. The requirement of Lorentz invariance generates an entanglement between the force and noise terms so that the noise itself should not be a covariant quantity. (author)
Equational theories of tropical sernirings
Aceto, Luca; Esik, Zoltan; Ingolfsdottir, Anna
2003-01-01
examples of such structures are the (max,+) semiring and the tropical semiring. It is shown that none of the exotic semirings commonly considered in the literature has a finite basis for its equations, and that similar results hold for the commutative idempotent weak semirings that underlie them. For each......This paper studies the equational theories of various exotic semirings presented in the literature. Exotic semirings are semirings whose underlying carrier set is some subset of the set of real numbers equipped with binary operations of minimum or maximum as sum, and addition as product. Two prime...... of these commutative idempotent weak semirings, the paper offers characterizations of the equations that hold in them, decidability results for their equational theories, explicit descriptions of the free algebras in the varieties they generate, and relative axiomatization results. Udgivelsesdato: APR 11...
Wave equations for pulse propagation
Shore, B.W.
1987-01-01
Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation
Feynman integrals and difference equations
Moch, S.; Schneider, C.
2007-09-01
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called ΠΣ * -fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)
Hidden Statistics of Schroedinger Equation
Zak, Michail
2011-01-01
Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.
Feynman integrals and difference equations
Moch, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation
2007-09-15
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called {pi}{sigma}{sup *}-fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)
Numerical solution of Boltzmann's equation
Sod, G.A.
1976-04-01
The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig
Computational partial differential equations using Matlab
Li, Jichun
2008-01-01
Brief Overview of Partial Differential Equations The parabolic equations The wave equations The elliptic equations Differential equations in broader areasA quick review of numerical methods for PDEsFinite Difference Methods for Parabolic Equations Introduction Theoretical issues: stability, consistence, and convergence 1-D parabolic equations2-D and 3-D parabolic equationsNumerical examples with MATLAB codesFinite Difference Methods for Hyperbolic Equations IntroductionSome basic difference schemes Dissipation and dispersion errors Extensions to conservation lawsThe second-order hyperbolic PDE
Linear determining equations for differential constraints
Kaptsov, O V
1998-01-01
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical determining equations used in the search for admissible Lie operators. As applications of this approach equations of an ideal incompressible fluid and non-linear heat equations are discussed
Equationally Compact Acts : Coproducts / Peeter Normak
Normak, Peeter
1998-01-01
In this article equational compactness of acts and its generalizations are discussed. As equational compactness does not carry over to coproducts a slight generalization of c-equational campactness is introduced. It is proved that a coproduct of acts is c-equationally compact if and only if all components are c-equationally campact
Exact results for the Boltzmann equation and Smoluchowski's coagulation equation
Hendriks, E.M.
1983-01-01
Almost no analytical solutions have been found for realistic intermolecular forces, largely due to the complicated structure of the collision term which calls for the construction of simplified models, in which as many physical properties are maintained as possible. In the first three chapters of this thesis such model Boltzmann equations are studied. Only spatially homogeneous gases with isotropic distribution functions are considered. Chapter I considers transition kernels, chapter II persistent scattering models and chapter III very hard particles. The second part of this dissertation deals with Smoluchowski's coagulation equation for the size distribution function in a coagulating system, with chapters devoted to the following topics: kinetics of gelation and universality, coagulation equations with gelation and exactly soluble models of nucleation. (Auth./C.F.)
Abstract methods in partial differential equations
Carroll, Robert W
2012-01-01
Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.
Linear integral equations and soliton systems
Quispel, G.R.W.
1983-01-01
A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)
ON THE EQUIVALENCE OF THE ABEL EQUATION
无
2006-01-01
This article uses the reflecting function of Mironenko to study some complicated differential equations which are equivalent to the Abel equation. The results are applied to discuss the behavior of solutions of these complicated differential equations.
Exact solitary waves of the Fisher equation
Kudryashov, Nikolai A.
2005-01-01
New method is presented to search exact solutions of nonlinear differential equations. This approach is used to look for exact solutions of the Fisher equation. New exact solitary waves of the Fisher equation are given
How to obtain the covariant form of Maxwell's equations from the continuity equation
Heras, Jose A
2009-01-01
The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations
How to obtain the covariant form of Maxwell's equations from the continuity equation
Heras, Jose A [Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana, Unidad Azcapotzalco, Av. San Pablo No. 180, Col. Reynosa, 02200, Mexico D. F. (Mexico); Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prolongacion Paseo de la Reforma 880, Mexico D. F. 01210 (Mexico)
2009-07-15
The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.
Extraction of dynamical equations from chaotic data
Rowlands, G.; Sprott, J.C.
1991-02-01
A method is described for extracting from a chaotic time series a system of equations whose solution reproduces the general features of the original data even when these are contaminated with noise. The equations facilitate calculation of fractal dimension, Lyapunov exponents and short-term predictions. The method is applied to data derived from numerical solutions of the Logistic equation, the Henon equations, the Lorenz equations and the Roessler equations. 10 refs., 5 figs
First-order partial differential equations
Rhee, Hyun-Ku; Amundson, Neal R
2001-01-01
This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of mo
Differential equations, mechanics, and computation
Palais, Richard S
2009-01-01
This book provides a conceptual introduction to the theory of ordinary differential equations, concentrating on the initial value problem for equations of evolution and with applications to the calculus of variations and classical mechanics, along with a discussion of chaos theory and ecological models. It has a unified and visual introduction to the theory of numerical methods and a novel approach to the analysis of errors and stability of various numerical solution algorithms based on carefully chosen model problems. While the book would be suitable as a textbook for an undergraduate or elementary graduate course in ordinary differential equations, the authors have designed the text also to be useful for motivated students wishing to learn the material on their own or desiring to supplement an ODE textbook being used in a course they are taking with a text offering a more conceptual approach to the subject.
Generalized equations of gravitational field
Stanyukovich, K.P.; Borisova, L.B.
1985-01-01
Equations for gravitational fields are obtained on the basis of a generalized Lagrangian Z=f(R) (R is the scalar curvature). Such an approach permits to take into account the evolution of a gravitation ''constant''. An expression for the force Fsub(i) versus the field variability is obtained. Conservation laws are formulated differing from the standard ones by the fact that in the right part of new equations the value Fsub(i) is present that goes to zero at an ultimate passage to the standard Einstein theory. An equation of state is derived for cosmological metrics for a particular case, f=bRsup(1+α) (b=const, α=const)
Numerical optimization using flow equations
Punk, Matthias
2014-12-01
We develop a method for multidimensional optimization using flow equations. This method is based on homotopy continuation in combination with a maximum entropy approach. Extrema of the optimizing functional correspond to fixed points of the flow equation. While ideas based on Bayesian inference such as the maximum entropy method always depend on a prior probability, the additional step in our approach is to perform a continuous update of the prior during the homotopy flow. The prior probability thus enters the flow equation only as an initial condition. We demonstrate the applicability of this optimization method for two paradigmatic problems in theoretical condensed matter physics: numerical analytic continuation from imaginary to real frequencies and finding (variational) ground states of frustrated (quantum) Ising models with random or long-range antiferromagnetic interactions.
Quantum Gross-Pitaevskii Equation
Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete
2017-07-01
Full Text Available We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.
Introductory course on differential equations
Gorain, Ganesh C
2014-01-01
Introductory Course on DIFFERENTIAL EQUATIONS provides an excellent exposition of the fundamentals of ordinary and partial differential equations and is ideally suited for a first course of undergraduate students of mathematics, physics and engineering. The aim of this book is to present the elementary theories of differential equations in the forms suitable for use of those students whose main interest in the subject are based on simple mathematical ideas. KEY FEATURES: Discusses the subject in a systematic manner without sacrificing mathematical rigour. A variety of exercises drill the students in problem solving in view of the mathematical theories explained in the book. Worked out examples illustrated according to the theories developed in the book with possible alternatives. Exhaustive collection of problems and the simplicity of presentation differentiate this book from several others. Material contained will help teachers as well as aspiring students of different competitive examinations.
The respiratory system in equations
Maury, Bertrand
2013-01-01
The book proposes an introduction to the mathematical modeling of the respiratory system. A detailed introduction on the physiological aspects makes it accessible to a large audience without any prior knowledge on the lung. Different levels of description are proposed, from the lumped models with a small number of parameters (Ordinary Differential Equations), up to infinite dimensional models based on Partial Differential Equations. Besides these two types of differential equations, two chapters are dedicated to resistive networks, and to the way they can be used to investigate the dependence of the resistance of the lung upon geometrical characteristics. The theoretical analysis of the various models is provided, together with state-of-the-art techniques to compute approximate solutions, allowing comparisons with experimental measurements. The book contains several exercises, most of which are accessible to advanced undergraduate students.
Dynamics of partial differential equations
Wayne, C Eugene
2015-01-01
This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties, and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equ...
Evolution equations for Killing fields
Coll, B.
1977-01-01
The problem of finding necessary and sufficient conditions on the Cauchy data for Einstein equations which insure the existence of Killing fields in a neighborhood of an initial hypersurface has been considered recently by Berezdivin, Coll, and Moncrief. Nevertheless, it can be shown that the evolution equations obtained in all these cases are of nonstrictly hyperbolic type, and, thus, the Cauchy data must belong to a special class of functions. We prove here that, for the vacuum and Einstein--Maxwell space--times and in a coordinate independent way, one can always choose, as evolution equations for the Killing fields, a strictly hyperbolic system: The above theorems can be thus extended to all Cauchy data for which the Einstein evolution problem has been proved to be well set
Quasisymmetry equations for conventional stellarators
Pustovitov, V.D.
1994-11-01
General quasisymmetry condition, which demands the independence of B 2 on one of the angular Boozer coordinates, is reduced to two equations containing only geometrical characteristics and helical field of a stellarator. The analysis is performed for conventional stellarators with a planar circular axis using standard stellarator expansion. As a basis, the invariant quasisymmetry condition is used. The quasisymmetry equations for stellarators are obtained from this condition also in an invariant form. Simplified analogs of these equations are given for the case when averaged magnetic surfaces are circular shifted torii. It is shown that quasisymmetry condition can be satisfied, in principle, in a conventional stellarator by a proper choice of two satellite harmonics of the helical field in addition to the main harmonic. Besides, there appears a restriction on the shift of magnetic surfaces. Thus, in general, the problem is closely related with that of self-consistent description of a configuration. (author)
The generalized good cut equation
Adamo, T M; Newman, E T
2010-01-01
The properties of null geodesic congruences (NGCs) in Lorentzian manifolds are a topic of considerable importance. More specifically NGCs with the special property of being shear-free or asymptotically shear-free (as either infinity or a horizon is approached) have received a great deal of recent attention for a variety of reasons. Such congruences are most easily studied via solutions to what has been referred to as the 'good cut equation' or the 'generalization good cut equation'. It is the purpose of this paper to study these equations and show their relationship to each other. In particular we show how they all have a four-complex-dimensional manifold (known as H-space, or in a special case as complex Minkowski space) as a solution space.
Integration rules for scattering equations
Baadsgaard, Christian; Bjerrum-Bohr, N.E.J.; Bourjaily, Jacob L.; Damgaard, Poul H.
2015-01-01
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Home; Journals; Pramana – Journal of Physics; Volume 79; Issue 1. Coupled Higgs ﬁeld equation and ... School of Mathematics and Computer Applications, Thapar University, Patiala 147 004, India; Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Distt. Solan 173 234, India ...
Coupled Higgs field equation and Hamiltonian amplitude equation ...
the rational functions are obtained. Keywords. ... differential equations as is evident by the number of research papers, books and a new symbolic software .... Now using (2.11), (2.14) in (2.8) with C1 = 0 and integrating once we get. P. 2 = − β.
Kahana, S.
1986-01-01
The role of the nuclear equation of state in determining the fate of the collapsing cores of massive stars is examined in light of both recent theoretical advances in this subject and recent experimental measurements with relativistic heavy ions. The difficulties existing in attempts to bring the softer nuclear matter apparently required by the theory of Type II supernovae into consonance with the heavy ion data are discussed. Relativistic mean field theory is introduced as a candidate for derivation of the equation of state, and a simple form for the saturation compressibility is obtained. 28 refs., 4 figs., 1 tab
Kinetic equations with pairing correlations
Fauser, R.
1995-12-01
The Gorkov equations are derived for a general non-equilibrium system. The Gorkov factorization is generalized by the cumulant expansion of the 2-particle correlation and by a generalized Wick theorem in the case of a perturbation expansion. A stationary solution for the Green functions in the Schwinger-Keldysh formalism is presented taking into account pairing correlations. Especially the effects of collisional broadening on the spectral functions and Green functions is discussed. Kinetic equations are derived in the quasi-particle approximation and in the case of particles with width. Explicit expressions for the self-energies are given. (orig.)
Partial differential equations an introduction
Colton, David
2004-01-01
Intended for a college senior or first-year graduate-level course in partial differential equations, this text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include coverage of integral equations and basic scattering theory. This complete and accessible treatment includes a variety of examples of inverse problems arising from improperly posed applications. Exercises at the ends of chapters, many with answers, offer a clear progression in developing an understanding of
Geometric approach to soliton equations
Sasaki, R.
1979-09-01
A class of nonlinear equations that can be solved in terms of nxn scattering problem is investigated. A systematic geometric method of exploiting conservation laws and related equations, the so-called prolongation structure, is worked out. The nxn problem is reduced to nsub(n-1)x(n-1) problems and finally to 2x2 problems, which have been comprehensively investigated recently by the author. A general method of deriving the infinite numbers of polynomial conservation laws for an nxn problem is presented. The cases of 3x3 and 2x2 problems are discussed explicitly. (Auth.)
Sensitivity for the Smoluchowski equation
Bailleul, I F
2011-01-01
This paper investigates the question of sensitivity of the solutions μ λ t of the Smoluchowski equation on R + * with respect to the parameters λ in the interaction kernel K λ . It is proved that μ λ t is a C 1 function of (t, λ) with values in a good space of measures under the hypotheses K λ (x, y) ≤ ψ(x) ψ(y), for some sub-linear function ψ, and ∫ψ 4+ε (x) μ 0 (dx) < ∞, and that the derivative is the unique solution of a related equation.
Basic linear partial differential equations
Treves, Francois
1975-01-01
Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students features most of the basic classical results. The methods, however, are decidedly nontraditional: in practically every instance, they tend toward a high level of abstraction. This approach recalls classical material to contemporary analysts in a language they can understand, as well as exploiting the field's wealth of examples as an introduction to modern theories.The four-part treatment covers the basic examples of linear partial differential equations and their
Kahana, S.
1986-01-01
The role of the nuclear equation of state in determining the fate of the collapsing cores of massive stars is examined in light of both recent theoretical advances in this subject and recent experimental measurements with relativistic heavy ions. The difficulties existing in attempts to bring the softer nuclear matter apparently required by the theory of Type II supernovae into consonance with the heavy ion data are discussed. Relativistic mean field theory is introduced as a candidate for derivation of the equation of state, and a simple form for the saturation compressibility is obtained. 28 refs., 4 figs., 1 tab.
Solution of the Baxter equation
Janik, R.A.
1996-01-01
We present a method of construction of a family of solutions of the Baxter equation arising in the Generalized Leading Logarithmic Approximation (GLLA) of the QCD pomeron. The details are given for the exchange of N = 2 reggeons but everything can be generalized in a straightforward way to arbitrary N. A specific choice of solutions is shown to reproduce the correct energy levels for half integral conformal weights. It is shown that the Baxter's equation must be supplemented by an additional condition on the solution. (author)
Fundamentals of equations of state
Eliezer, Shalom; Hora, Heinrich
2002-01-01
The equation of state was originally developed for ideal gases, and proved central to the development of early molecular and atomic physics. Increasingly sophisticated equations of state have been developed to take into account molecular interactions, quantization, relativistic effects, etc. Extreme conditions of matter are encountered both in nature and in the laboratory, for example in the centres of stars, in relativistic collisions of heavy nuclei, in inertial confinement fusion (where a temperature of 10 9 K and a pressure exceeding a billion atmospheres can be achieved). A sound knowledg
Nielsen number and differential equations
Andres Jan
2005-01-01
Full Text Available In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations, two main approaches are presented. The first is via Poincaré's translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links with the Sharkovskii-like theorems (a finite number of periodic solutions imply infinitely many subharmonics are indicated, jointly with some further consequences like the nontrivial -structure of solutions of initial value problems. Some illustrating examples are supplied and open problems are formulated.
Applied analysis and differential equations
Cârj, Ovidiu
2007-01-01
This volume contains refereed research articles written by experts in the field of applied analysis, differential equations and related topics. Well-known leading mathematicians worldwide and prominent young scientists cover a diverse range of topics, including the most exciting recent developments. A broad range of topics of recent interest are treated: existence, uniqueness, viability, asymptotic stability, viscosity solutions, controllability and numerical analysis for ODE, PDE and stochastic equations. The scope of the book is wide, ranging from pure mathematics to various applied fields such as classical mechanics, biomedicine, and population dynamics.
Sequent Calculus and Equational Programming
Nicolas Guenot
2015-07-01
Full Text Available Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.
Radar equations for modern radar
Barton, David K
2012-01-01
Based on the classic Radar Range-Performance Analysis from 1980, this practical volume extends that work to ensure applicability of radar equations to the design and analysis of modern radars. This unique book helps you identify what information on the radar and its environment is needed to predict detection range. Moreover, it provides equations and data to improve the accuracy of range calculations. You find detailed information on propagation effects, methods of range calculation in environments that include clutter, jamming and thermal noise, as well as loss factors that reduce radar perfo
Equating accelerometer estimates among youth
Brazendale, Keith; Beets, Michael W; Bornstein, Daniel B
2016-01-01
from one set of cutpoints into another. Bland Altman plots illustrate the agreement between actual MVPA and predicted MVPA values. RESULTS: Across the total sample, mean MVPA ranged from 29.7MVPAmind(-1) (Puyau) to 126.1MVPAmind(-1) (Freedson 3 METs). Across conversion equations, median absolute...
Variational linear algebraic equations method
Moiseiwitsch, B.L.
1982-01-01
A modification of the linear algebraic equations method is described which ensures a variational bound on the phaseshifts for potentials having a definite sign at all points. The method is illustrated by the elastic scattering of s-wave electrons by the static field of atomic hydrogen. (author)
Integrodifferential equation approach. Pt. 1
Oehm, W.; Sofianos, S.A.; Fiedeldey, H.; South Africa Univ., Pretoria. Dept. of Physics); Fabre de la Ripelle, M.; South Africa Univ., Pretoria. Dept. of Physics)
1990-02-01
A single integrodifferential equation in two variables, valid for A nucleons interacting by pure Wigner forces, which has previously only been solved in the extreme and uncoupled adiabatic approximations is now solved exactly for three- and four-nucleon systems. The results are in good agreement with the values obtained for the binding energies by means of an empirical interpolation formula. This validates all our previous conclusions, in particular that the omission of higher (than two) order correlations in our four-body equation only produces a rather small underbinding. The integrodifferential equation approach (IDEA) is here also extended to spin-dependent forces of the Malfliet-Tjon type, resulting in two coupled integrodifferential equations in two variables. The exact solution and the interpolated adiabatic approximation are again in good agreement. The inclusion of the hypercentral part of the two-body interaction in the definition of the Faddeev-type components again leads to substantial improvement for fully local potentials, acting in all partial waves. (orig.)
A generalized advection dispersion equation
This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of.
Nonlocal higher order evolution equations
Rossi, Julio D.; Schö nlieb, Carola-Bibiane
2010-01-01
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove
Crowe, C.T.
1975-01-01
General features of a vapor-droplet flow are discussed and the equations expressing the conservation of mass, momentum, and energy for the vapor, liquid, and mixture using the control volume approach are derived. The phenomenological laws describing the exchange of mass, momentum, and energy between phases are also reviewed. The results have application to development of water-dominated geothermal resources
On the Saha Ionization Equation
the equation in terms of rate theory. ... that the said theory is said to be the harbinger of modern astro- ... Parichay (An Introduction to the Universe). Tagore ..... where |e| is the magnitude of the electron's charge and E is the electric field intensity ...
Saha equation in Rindler space
Sanchari De
2017-05-31
May 31, 2017 ... scenario, the flat local geometry is called the Rindler space. For an illustration, let us consider two reference ... the local acceleration of the frame. To investigate Saha equation in a uniformly acceler- ... the best of our knowledge, the study of Saha equa- tion in Rindler space has not been reported earlier.
Slave equations for spin models
Catterall, S.M.; Drummond, I.T.; Horgan, R.R.
1992-01-01
We apply an accelerated Langevin algorithm to the simulation of continuous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models. (orig.)
Pendulum Motion and Differential Equations
Reid, Thomas F.; King, Stephen C.
2009-01-01
A common example of real-world motion that can be modeled by a differential equation, and one easily understood by the student, is the simple pendulum. Simplifying assumptions are necessary for closed-form solutions to exist, and frequently there is little discussion of the impact if those assumptions are not met. This article presents a…
Elizarova, Tatiana G
2009-01-01
This book presents two interconnected mathematical models generalizing the Navier-Stokes system. The models, called the quasi-gas-dynamic and quasi-hydrodynamic equations, are then used as the basis of numerical methods solving gas- and fluid-dynamic problems.
Stability of Functional Differential Equations
Lemm, Jeffrey M
1986-01-01
This book provides an introduction to the structure and stability properties of solutions of functional differential equations. Numerous examples of applications (such as feedback systrems with aftereffect, two-reflector antennae, nuclear reactors, mathematical models in immunology, viscoelastic bodies, aeroautoelastic phenomena and so on) are considered in detail. The development is illustrated by numerous figures and tables.
Quantum adiabatic Markovian master equations
Albash, Tameem; Zanardi, Paolo; Boixo, Sergio; Lidar, Daniel A
2012-01-01
We develop from first principles Markovian master equations suited for studying the time evolution of a system evolving adiabatically while coupled weakly to a thermal bath. We derive two sets of equations in the adiabatic limit, one using the rotating wave (secular) approximation that results in a master equation in Lindblad form, the other without the rotating wave approximation but not in Lindblad form. The two equations make markedly different predictions depending on whether or not the Lamb shift is included. Our analysis keeps track of the various time and energy scales associated with the various approximations we make, and thus allows for a systematic inclusion of higher order corrections, in particular beyond the adiabatic limit. We use our formalism to study the evolution of an Ising spin chain in a transverse field and coupled to a thermal bosonic bath, for which we identify four distinct evolution phases. While we do not expect this to be a generic feature, in one of these phases dissipation acts to increase the fidelity of the system state relative to the adiabatic ground state. (paper)
Weak solutions of magma equations
Krishnan, E.V.
1999-01-01
Periodic solutions in terms of Jacobian cosine elliptic functions have been obtained for a set of values of two physical parameters for the magma equation which do not reduce to solitary-wave solutions. It was also obtained solitary-wave solutions for another set of these parameters as an infinite period limit of periodic solutions in terms of Weierstrass and Jacobian elliptic functions
Wave-equation dispersion inversion
Li, Jing
2016-12-08
We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.
Solutions of Einstein's field equations
Tomonaga, Y [Utsunomiya Univ. (Japan). Faculty of Education
1978-12-01
In this paper the author investigates the Einstein's field equations of the non-vacuum case and generalizes the solution of Robertson-Walker by the three dimensional Einstein spaces. In Section 2 the author shortly generalizes the dynamic space-time of G. Lemetre and A. Friedmann by a simple transformation.
Equations for formally real meadows
Bergstra, J.A.; Bethke, I.; Ponse, A.
2015-01-01
We consider the signatures Σm = (0,1,−,+,⋅,−1) of meadows and (Σm,s) of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these signatures. In the first case, we extend the axiomatization of zero-totalized fields by a single axiom
Wave equation of hydrogen atom
Suwito.
1977-01-01
The calculation of the energy levels of the hydrogen atom using Bohr, Schroedinger and Dirac theories is reviewed. The result is compared with that obtained from infinite component wave equations theory which developed recently. The conclusion can be stated that the latter theory is better to describe the composit system than the former. (author)
Transport equation and shock waves
Besnard, D.
1981-04-01
A multi-group method is derived from a one dimensional transport equation for the slowing down and spatial transport of energetic positive ions in a plasma. This method is used to calculate the behaviour of energetic charged particles in non homogeneous and non stationary plasma, and the effect of energy deposition of the particles on the heating of the plasma. In that purpose, an equation for the density of fast ions is obtained from the Fokker-Planck equation, and a closure condition for the second moment of this equation is deduced from phenomenological considerations. This method leads to a numerical method, simple and very efficient, which doesn't require much computer storage. Two types of numerical results are obtained. First, results on the slowing down of 3.5 MeV alpha particles in a 50 keV plasma plublished by Corman and al and Moses are compared with the results obtained with both our method and a Monte Carlo type method. Good agreement was obtained, even for energy deposition on the ions of the plasma. Secondly, we have calculated propagation of alpha particles heating a cold plasma. These results are in very good agreement with those given by an accurate Monte Carlo method, for both the thermal velocity, and the energy deposition in the plasma
Structural equations in language learning
Moortgat, M.J.
In categorial systems with a fixed structural component, the learning problem comes down to finding the solution for a set of typeassignment equations. A hard-wired structural component is problematic if one want to address issues of structural variation. Our starting point is a type-logical
Fractional Diffusion Equations and Anomalous Diffusion
Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin
2018-01-01
Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.
Painleve test and discrete Boltzmann equations
Euler, N.; Steeb, W.H.
1989-01-01
The Painleve test for various discrete Boltzmann equations is performed. The connection with integrability is discussed. Furthermore the Lie symmetry vector fields are derived and group-theoretical reduction of the discrete Boltzmann equations to ordinary differentiable equations is performed. Lie Backlund transformations are gained by performing the Painleve analysis for the ordinary differential equations. 16 refs
Plas, R.
1962-07-01
The author reports a study on kinetics equations for a reactor. He uses the conventional form of these equations but by using a dynamic multiplication factor. Thus, constants related to delayed neutrons are not modified by efficiency factors. The author first describes the theoretic kinetic operation of a reactor and develops the associated equations. He reports the development of equations for multiplication factors.
Algebraic entropy for differential-delay equations
Viallet, Claude M.
2014-01-01
We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce differential-delay equations with vanishing entropy from known integrable differential-difference equations.
Invariant imbedding equations for linear scattering problems
Apresyan, L.
1988-01-01
A general form of the invariant imbedding equations is investigated for the linear problem of scattering by a bounded scattering volume. The conditions for the derivability of such equations are described. It is noted that the possibility of the explicit representation of these equations for a sphere and for a layer involves the separation of variables in the unperturbed wave equation
The AGL equation from the dipole picture
Gay Ducati, M.B.; Goncalves, V.P.
1999-01-01
The AGL equation includes all multiple pomeron exchanges in the double logarithmic approximation (DLA) limit, leading to a unitarized gluon distribution in the small x regime. This equation was originally obtained using the Glauber-Mueller approach. We demonstrate in this paper that the AGL equation and, consequently, the GLR equation, can also be obtained from the dipole picture in the double logarithmic limit, using an evolution equation, recently proposed, which includes all multiple pomeron exchanges in the leading logarithmic approximation. Our conclusion is that the AGL equation is a good candidate for a unitarized evolution equation at small x in the DLA limit
Thermoviscous Model Equations in Nonlinear Acoustics
Rasmussen, Anders Rønne
Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....
Manhattan equation for the operational amplifier
Mishonov, Todor M.; Danchev, Victor I.; Petkov, Emil G.; Gourev, Vassil N.; Dimitrova, Iglika M.; Varonov, Albert M.
2018-01-01
A differential equation relating the voltage at the output of an operational amplifier $U_0$ and the difference between the input voltages ($U_{+}$ and $U_{-}$) has been derived. The crossover frequency $f_0$ is a parameter in this operational amplifier master equation. The formulas derived as a consequence of this equation find applications in thousands of specifications for electronic devices but as far as we know, the equation has never been published. Actually, the master equation of oper...
Reduced kinetic equations: An influence functional approach
Wio, H.S.
1985-01-01
The author discusses a scheme for obtaining reduced descriptions of multivariate kinetic equations based on the 'influence functional' method of Feynmann. It is applied to the case of Fokker-Planck equations showing the form that results for the reduced equation. The possibility of Markovian or non-Markovian reduced description is discussed. As a particular example, the reduction of the Kramers equation to the Smoluchwski equation in the limit of high friction is also discussed
Dynamical equations for the optical potential
Kowalski, K.L.
1981-01-01
Dynamical equations for the optical potential are obtained starting from a wide class of N-particle equations. This is done with arbitrary multiparticle interactions to allow adaptation to few-body models of nuclear reactions and including all effects of nucleon identity. Earlier forms of the optical potential equations are obtained as special cases. Particular emphasis is placed upon obtaining dynamical equations for the optical potential from the equations of Kouri, Levin, and Tobocman including all effects of particle identity
Group foliation of finite difference equations
Thompson, Robert; Valiquette, Francis
2018-06-01
Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.
An inverse problem in a parabolic equation
Zhilin Li
1998-11-01
Full Text Available In this paper, an inverse problem in a parabolic equation is studied. An unknown function in the equation is related to two integral equations in terms of heat kernel. One of the integral equations is well-posed while another is ill-posed. A regularization approach for constructing an approximate solution to the ill-posed integral equation is proposed. Theoretical analysis and numerical experiment are provided to support the method.
Systems of Inhomogeneous Linear Equations
Scherer, Philipp O. J.
Many problems in physics and especially computational physics involve systems of linear equations which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the dimension of the system is not too large standard methods like Gaussian elimination or QR decomposition are sufficient. Systems with a tridiagonal matrix are important for cubic spline interpolation and numerical second derivatives. They can be solved very efficiently with a specialized Gaussian elimination method. Practical applications often involve very large dimensions and require iterative methods. Convergence of Jacobi and Gauss-Seidel methods is slow and can be improved by relaxation or over-relaxation. An alternative for large systems is the method of conjugate gradients.
MAGNETOHYDRODYNAMIC EQUATIONS (MHD GENERATION CODE
Francisco Frutos Alfaro
2017-04-01
Full Text Available A program to generate codes in Fortran and C of the full magnetohydrodynamic equations is shown. The program uses the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the magnetohydrodynamic equations to obtain a code that can be used as a seed for a magnetohydrodynamic code for numerical applications. As an example, we present part of the output of our programs for Cartesian coordinates and how to do the discretization.
Combinatorics of Generalized Bethe Equations
Kozlowski, Karol K.; Sklyanin, Evgeny K.
2013-10-01
A generalization of the Bethe ansatz equations is studied, where a scalar two-particle S-matrix has several zeroes and poles in the complex plane, as opposed to the ordinary single pole/zero case. For the repulsive case (no complex roots), the main result is the enumeration of all distinct solutions to the Bethe equations in terms of the Fuss-Catalan numbers. Two new combinatorial interpretations of the Fuss-Catalan and related numbers are obtained. On the one hand, they count regular orbits of the permutation group in certain factor modules over {{Z}^M}, and on the other hand, they count integer points in certain M-dimensional polytopes.
Nonlocal higher order evolution equations
Rossi, Julio D.
2010-06-01
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.
Numerical Solution of Parabolic Equations
Østerby, Ole
These lecture notes are designed for a one-semester course on finite-difference methods for parabolic equations. These equations which traditionally are used for describing diffusion and heat-conduction problems in Geology, Physics, and Chemistry have recently found applications in Finance Theory...... ? and how do boundary value approximations affect the overall order of the method. Knowledge of a reliable order and error estimate enables us to determine (near-)optimal step sizes to meet a prescribed error tolerance, and possibly to extrapolate to get (higher order and) better accuracy at a minimal...... expense. Problems in two space dimensions are effectively handled using the Alternating Direction Implicit (ADI) technique. We present a systematic way of incorporating inhomogeneous terms and derivative boundary conditions in ADI methods as well as mixed derivative terms....
Chiral equations and fiber bundles
Mateos, T.; Becerril, R.
1992-01-01
Using the hypothesis g = g (lambda i ), the chiral equations (rhog, z g -1 ), z -bar + (rhog, z -barg -1 ), z = 0 are reduced to a Killing equation of a p-dimensional space V p , being lambda i lambda i (z, z-bar) 'geodesic' parameters of V p . Supposing that g belongs to a Lie group G, one writes the corresponding Lie algebra elements (F) in terms of the Killing vectors of V p and the generators of the subalgebra of F of dimension d = dimension of the Killing space. The elements of the subalgebras belong to equivalence classes which in the respective group form a principal fiber bundle. This is used to integrate the matrix g in terms of the complex variables z and z-bar ( Author)
The equations icons of knowledge
Bais, Sander
2005-01-01
For thousands of years mankind has tried to understand nature. Exploring the world on all scales with instruments of ever more ingenuity, we have been able to unravel some of the great mysteries that surround us. While collecting an overwhelming multitude of observational facts, we discovered fundamental laws that govern the structure and evolution of physical reality. We know that nature speaks to us in the language of mathematics. In this language most of our basic understanding of the physical world can be expressed in an unambiguous and concise way. The most artificial language turns out to be the most natural of all. The laws of nature correspond to equations. These equations are the icons of knowledge that mark crucial turning points in our thinking about the world we happen to live in. They form the symbolic representation of most of what we know, and as such constitute an important and robust part of our culture.
Implementing Parquet equations using HPX
Kellar, Samuel; Wagle, Bibek; Yang, Shuxiang; Tam, Ka-Ming; Kaiser, Hartmut; Moreno, Juana; Jarrell, Mark
A new C++ runtime system (HPX) enables simulations of complex systems to run more efficiently on parallel and heterogeneous systems. This increased efficiency allows for solutions to larger simulations of the parquet approximation for a system with impurities. The relevancy of the parquet equations depends upon the ability to solve systems which require long runs and large amounts of memory. These limitations, in addition to numerical complications arising from stability of the solutions, necessitate running on large distributed systems. As the computational resources trend towards the exascale and the limitations arising from computational resources vanish efficiency of large scale simulations becomes a focus. HPX facilitates efficient simulations through intelligent overlapping of computation and communication. Simulations such as the parquet equations which require the transfer of large amounts of data should benefit from HPX implementations. Supported by the the NSF EPSCoR Cooperative Agreement No. EPS-1003897 with additional support from the Louisiana Board of Regents.
Handbook of structural equation modeling
Hoyle, Rick H
2012-01-01
The first comprehensive structural equation modeling (SEM) handbook, this accessible volume presents both the mechanics of SEM and specific SEM strategies and applications. The editor, contributors, and editorial advisory board are leading methodologists who have organized the book to move from simpler material to more statistically complex modeling approaches. Sections cover the foundations of SEM; statistical underpinnings, from assumptions to model modifications; steps in implementation, from data preparation through writing the SEM report; and basic and advanced applications, inclu
Bonny, J.; Fulton, M.
1983-01-01
The subject is discussed under the headings: comparison of world nuclear generating capacity forecasts; world uranium requirements; comparison of uranium production capability forecasts; supply and demand situation in 1990 and 1995; a perspective on the uranium equation (economic factors; development lead times as a factor affecting market stability; the influence of uncertainty; the uranium market in perspective; the uranium market in 1995). (U.K.)
Differential equations in airplane mechanics
Carleman, M T
1922-01-01
In the following report, we will first draw some conclusions of purely theoretical interest, from the general equations of motion. At the end, we will consider the motion of an airplane, with the engine dead and with the assumption that the angle of attack remains constant. Thus we arrive at a simple result, which can be rendered practically utilizable for determining the trajectory of an airplane descending at a constant steering angle.
Integration of Chandrasekhar's integral equation
Tanaka, Tasuku
2003-01-01
We solve Chandrasekhar's integration equation for radiative transfer in the plane-parallel atmosphere by iterative integration. The primary thrust in radiative transfer has been to solve the forward problem, i.e., to evaluate the radiance, given the optical thickness and the scattering phase function. In the area of satellite remote sensing, our problem is the inverse problem: to retrieve the surface reflectance and the optical thickness of the atmosphere from the radiance measured by satellites. In order to retrieve the optical thickness and the surface reflectance from the radiance at the top-of-the atmosphere (TOA), we should express the radiance at TOA 'explicitly' in the optical thickness and the surface reflectance. Chandrasekhar formalized radiative transfer in the plane-parallel atmosphere in a simultaneous integral equation, and he obtained the second approximation. Since then no higher approximation has been reported. In this paper, we obtain the third approximation of the scattering function. We integrate functions derived from the second approximation in the integral interval from 1 to ∞ of the inverse of the cos of zenith angles. We can obtain the indefinite integral rather easily in the form of a series expansion. However, the integrals at the upper limit, ∞, are not yet known to us. We can assess the converged values of those series expansions at ∞ through calculus. For integration, we choose coupling pairs to avoid unnecessary terms in the outcome of integral and discover that the simultaneous integral equation can be deduced to the mere integral equation. Through algebraic calculation, we obtain the third approximation as a polynomial of the third degree in the atmospheric optical thickness
Equation of State Project Overview
Crockett, Scott [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-09-11
A general overview of the Equation of State (EOS) Project will be presented. The goal is to provide the audience with an introduction of what our more advanced methods entail (DFT, QMD, etc.. ) and how these models are being utilized to better constrain the thermodynamic models. These models substantially reduce our regions of interpolation between the various thermodynamic limits. I will also present a variety example of recent EOS work.
Simple equation method for nonlinear partial differential equations and its applications
Taher A. Nofal
2016-04-01
Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.
Effective Schroedinger equations on submanifolds
Wachsmuth, Jakob
2010-02-11
In this thesis the time dependent Schroedinger equation is considered on a Riemannian manifold A with a potential that localizes a certain class of states close to a fixed submanifold C, the constraint manifold. When the potential is scaled in the directions normal to C by a small parameter epsilon, the solutions concentrate in an epsilon-neighborhood of the submanifold. An effective Schroedinger equation on the submanifold C is derived and it is shown that its solutions, suitably lifted to A, approximate the solutions of the original equation on A up to errors of order {epsilon}{sup 3} vertical stroke t vertical stroke at time t. Furthermore, it is proved that, under reasonable conditions, the eigenvalues of the corresponding Hamiltonians below a certain energy coincide upto errors of order {epsilon}{sup 3}. These results holds in the situation where tangential and normal energies are of the same order, and where exchange between normal and tangential energies occurs. In earlier results tangential energies were assumed to be small compared to normal energies, and rather restrictive assumptions were needed, to ensure that the separation of energies is maintained during the time evolution. The most important consequence of this thesis is that now constraining potentials that change their shape along the submanifold can be treated, which is the typical situation in applications like molecular dynamics and quantum waveguides.
Deriving the bond pricing equation
Kožul Nataša
2014-01-01
Full Text Available Given the recent focus on Eurozone debt crisis and the credit rating downgrade not only of US debt, but that of other countries and many UK major banking institutions, this paper aims to explain the concept of bond yield, its different measures and bond pricing equation. Yields on capital market instruments are rarely quoted on the same basis, which makes direct comparison between different as investment choices impossible. Some debt instruments are quoted on discount basis, whilst coupon-bearing ones accrue interest differently, offer different compounding opportunities, have different coupon payment frequencies, and manage non-business day maturity dates differently. Moreover, rules governing debt vary across countries, markets and currencies, making yield calculation and comparison a rather complex issue. Thus, some fundamental concepts applicable to debt instrument yield measurement, with focus on bond equation, are presented here. In addition, bond equation expressed in annuity form and used to apply Newton-Raphson algorithm to derive true bond yield is also shown.
Wave equations in higher dimensions
Dong, Shi-Hai
2011-01-01
Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativisti...
Geometric Implications of Maxwell's Equations
Smith, Felix T.
2015-03-01
Maxwell's synthesis of the varied results of the accumulated knowledge of electricity and magnetism, based largely on the searching insights of Faraday, still provide new issues to explore. A case in point is a well recognized anomaly in the Maxwell equations: The laws of electricity and magnetism require two 3-vector and two scalar equations, but only six dependent variables are available to be their solutions, the 3-vectors E and B. This leaves an apparent redundancy of two degrees of freedom (J. Rosen, AJP 48, 1071 (1980); Jiang, Wu, Povinelli, J. Comp. Phys. 125, 104 (1996)). The observed self-consistency of the eight equations suggests that they contain additional information. This can be sought as a previously unnoticed constraint connecting the space and time variables, r and t. This constraint can be identified. It distorts the otherwise Euclidean 3-space of r with the extremely slight, time dependent curvature k (t) =Rcurv-2 (t) of the 3-space of a hypersphere whose radius has the time dependence dRcurv / dt = +/- c nonrelativistically, or dRcurvLor / dt = +/- ic relativistically. The time dependence is exactly that of the Hubble expansion. Implications of this identification will be explored.
Five-dimensional Monopole Equation with Hedge-Hog Ansatz and Abel's Differential Equation
Kihara, Hironobu
2008-01-01
We review the generalized monopole in the five-dimensional Euclidean space. A numerical solution with the Hedge-Hog ansatz is studied. The Bogomol'nyi equation becomes a second order autonomous non-linear differential equation. The equation can be translated into the Abel's differential equation of the second kind and is an algebraic differential equation.
Partial differential equations of mathematical physics and integral equations
Guenther, Ronald B
1996-01-01
This book was written to help mathematics students and those in the physical sciences learn modern mathematical techniques for setting up and analyzing problems. The mathematics used is rigorous, but not overwhelming, while the authors carefully model physical situations, emphasizing feedback among a beginning model, physical experiments, mathematical predictions, and the subsequent refinement and reevaluation of the physical model itself. Chapter 1 begins with a discussion of various physical problems and equations that play a central role in applications. The following chapters take up the t
Handbook of differential equations stationary partial differential equations
Chipot, Michel
2006-01-01
This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Ke
Sugawara N
2014-02-01
Mifflin–St Jeor equations did not show a significant bias in the prediction of REE, however, a significant overestimation error was shown for the Food and Agriculture Organization/World Health Organization/United Nations University and Schofield equations. Conclusion: When estimating REE in patients with schizophrenia taking antipsychotics, the Harris–Benedict equation appears to be the most appropriate for clinical use. Keywords: indirect calorimetry, Japanese, Harris–Benedict equation, antipsychotics
Partial differential equations for scientists and engineers
Farlow, Stanley J
1993-01-01
Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th
Semilinear Schrödinger equations
Cazenave, Thierry
2003-01-01
The nonlinear Schrödinger equation has received a great deal of attention from mathematicians, in particular because of its applications to nonlinear optics. It is also a good model dispersive equation, since it is often technically simpler than other dispersive equations, such as the wave or Korteweg-de Vries equation. Particularly useful tools in studying the nonlinear Schrödinger equation are energy and Strichartz's estimates. This book presents various mathematical aspects of the nonlinear Schrödinger equation. It examines both problems of local nature (local existence of solutions, unique
Functional Fourier transforms and the loop equation
Bershadskii, M.A.; Vaisburd, I.D.; Migdal, A.A.
1986-01-01
The Migdal-Makeenko momentum-space loop equation is investigated. This equation is derived from the ordinary loop equation by taking the Fourier transform of the Wilson functional. A perturbation theory is constructed for the new equation and it is proved that the action of the loop operator is determined by vertex functions which coincide with those of the previous equation. It is shown how the ghost loop arises in direct iterations of the momentum-space equation with respect to the coupling constant. A simple example is used to illustrate the mechanism of appearance of an integration in the interior loops in transition to observables
International Workshop on Elliptic and Parabolic Equations
Schrohe, Elmar; Seiler, Jörg; Walker, Christoph
2015-01-01
This volume covers the latest research on elliptic and parabolic equations and originates from the international Workshop on Elliptic and Parabolic Equations, held September 10-12, 2013 at the Leibniz Universität Hannover. It represents a collection of refereed research papers and survey articles written by eminent scientist on advances in different fields of elliptic and parabolic partial differential equations, including singular Riemannian manifolds, spectral analysis on manifolds, nonlinear dispersive equations, Brownian motion and kernel estimates, Euler equations, porous medium type equations, pseudodifferential calculus, free boundary problems, and bifurcation analysis.
Lewis, Teresa V; Harrison, Donald L; Gildon, Brooke L; Carter, Sandra M; Turman, Martin A
2016-06-01
To determine if significant correlations exist between glomerular filtration rate (GFR) prediction equation values, derived by using the original Schwartz equation and the Chronic Kidney Disease in Children (CKiD) bedside equation with a 24-hour urine creatinine clearance (Clcr ) value normalized to a body surface area of 1.73 m(2) in overweight and obese children. Prospective analysis (20 patients) and retrospective analysis (43 patients). Pediatric inpatient ward and pediatric nephrology clinic at a comprehensive academic medical center. Sixty-three pediatric patients (aged 5-17 years), of whom 27 were overweight (body mass index [BMI] at the 85th percentile or higher) and 36 were not overweight (BMI lower than the 85th percentile [controls]) between 2007 and 2012. Data from the overweight patients were compared with nonoverweight controls. GFR values were calculated by using the original Schwartz equation and the CKiD bedside equation. Each patient's 24-hour urine Clcr value normalized to a body surface area of 1.73 m(2) served as the index value. A Pearson correlation coefficient model was used to determine association between the 24-hour urine Clcr value (index value) with the Schwartz and CKiD GFR estimations. Significant correlation was found to exist between the Schwartz and CKiD bedside GFR estimations relative to the 24-hour urine Clcr in the control subjects (r = 0.85, poverweight subjects (r = 0.86, poverweight children with a kidney disorder. The CKiD bedside GFR estimations were not significantly different compared with 24-hour urine Clcr values for the overweight group with kidney disorder (p=0.85). The Schwartz and CKiD bedside estimations of GFR correlated with 24-hour urine Clcr values in both overweight and nonoverweight children. Compared with the Schwartz equation, which tended to overestimate renal function, the CKiD bedside equation appeared to approximate 24-hour urine Clcr more closely in overweight children with kidney disorder. © 2016
Validation of predictive equations for glomerular filtration rate in the Saudi population
Al Wakeel Jamal
2009-01-01
Full Text Available Predictive equations provide a rapid method of assessing glomerular filtration rate (GFR. To compare the various predictive equations for the measurement of this parameter in the Saudi population, we measured GFR by the Modification of Diet in Renal Disease (MDRD and Cockcroft-Gault formulas, cystatin C, reciprocal of cystatin C, creatinine clearance, reciprocal of creatinine, and inulin clearance in 32 Saudi subjects with different stages of renal disease. We com-pared GFR measured by inulin clearance and the estimated GFR by the equations. The study included 19 males (59.4% and 13 (40.6% females with a mean age of 42.3 ± 15.2 years and weight of 68.6 ± 17.7 kg. The mean serum creatinine was 199 ± 161 μmol/L. The GFR measured by inulin clearance was 50.9 ± 33.5 mL/min, and the estimated by Cockcroft-Gault and by MDRD equations was 56.3 ± 33.3 and 52.8 ± 32.0 mL/min, respectively. The GFR estimated by MDRD revealed the strongest correlation with the measured inulin clearance (r= 0.976, P= 0.0000 followed by the GFR estimated by Cockcroft-Gault, serum cystatin C, and serum creatinine (r= 0.953, P= 0.0000 (r= 0.787, P= 0.0001 (r= -0.678, P= 0.001, respectively. The reciprocal of cystatin C and serum creatinine revealed a correlation coefficient of 0.826 and 0.93, respectively. Cockroft-Gault for-mula overestimated the GFR by 5.40 ± 10.3 mL/min in comparison to the MDRD formula, which exhibited the best correlation with inulin clearance in different genders, age groups, body mass index, renal transplant recipients, chronic kidney disease stages when compared to other GFR predictive equations.
Zhao, Zhonglong; Zhang, Yufeng; Han, Zhong; Rui, Wenjuan
2014-01-01
In this paper, the simplest equation method is used to construct exact traveling solutions of the (3+1)-dimensional KP equation and generalized Fisher equation. We summarize the main steps of the simplest equation method. The Bernoulli and Riccati equation are used as simplest equations. This method is straightforward and concise, and it can be applied to other nonlinear partial differential equations
Kotel'nikov, G.A.
1994-01-01
An algorithm id proposed for research the symmetries of mathematical physics equation. The application of this algorithm to the Schroedinger equation permitted to establish, that in addition to the known symmetry the Schroedinger equation possesses also the relativistic symmetry
Savoye, Philippe
2009-01-01
In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.
Reduction of lattice equations to the Painlevé equations: PIV and PV
Nakazono, Nobutaka
2018-02-01
In this paper, we construct a new relation between Adler-Bobenko-Suris equations and Painlevé equations. Moreover, using this connection we construct the difference-differential Lax representations of the fourth and fifth Painlevé equations.
Is paediatric trauma severity overestimated at triage?
DO, H Q; Hesselfeldt, R; Steinmetz, J
2014-01-01
BACKGROUND: Severe paediatric trauma is rare, and pre-hospital and local hospital personnel experience with injured children is often limited. We hypothesised that a higher proportion of paediatric trauma victims were taken to the regional trauma centre (TC). METHODS: This is an observational...... follow-up study that involves one level I TC and seven local hospitals. We included paediatric (trauma patients with a driving distance to the TC > 30 minutes. The primary end-point was the proportion of trauma patients arriving in the TC. RESULTS: We included 1934...... trauma patients, 238 children and 1696 adults. A total of 33/238 children (13.9%) vs. 304/1696 adults (17.9%) were transported to the TC post-injury (P = 0.14). Among these, children were significantly less injured than adults [median Injury Severity Score (ISS) 9 vs. 14, P
Meiofauna metabolism in suboxic sediments: currently overestimated.
Ulrike Braeckman
Full Text Available Oxygen is recognized as a structuring factor of metazoan communities in marine sediments. The importance of oxygen as a controlling factor on meiofauna (32 µm-1 mm in size respiration rates is however less clear. Typically, respiration rates are measured under oxic conditions, after which these rates are used in food web studies to quantify the role of meiofauna in sediment carbon turnover. Sediment oxygen concentration ([O(2] is generally far from saturated, implying that (1 current estimates of the role of meiofauna in carbon cycling may be biased and (2 meiofaunal organisms need strategies to survive in oxygen-stressed environments. Two main survival strategies are often hypothesized: 1 frequent migration to oxic layers and 2 morphological adaptation. To evaluate these hypotheses, we (1 used a model of oxygen turnover in the meiofauna body as a function of ambient [O(2], and (2 performed respiration measurements at a range of [O(2] conditions. The oxygen turnover model predicts a tight coupling between ambient [O(2] and meiofauna body [O(2] with oxygen within the body being consumed in seconds. This fast turnover favors long and slender organisms in sediments with low ambient [O(2] but even then frequent migration between suboxic and oxic layers is for most organisms not a viable strategy to alleviate oxygen limitation. Respiration rates of all measured meiofauna organisms slowed down in response to decreasing ambient [O(2], with Nematoda displaying the highest metabolic sensitivity for declining [O(2] followed by Foraminifera and juvenile Gastropoda. Ostracoda showed a behavioral stress response when ambient [O(2] reached a critical level. Reduced respiration at low ambient [O(2] implies that meiofauna in natural, i.e. suboxic, sediments must have a lower metabolism than inferred from earlier respiration rates conducted under oxic conditions. The implications of these findings are discussed for the contribution of meiofauna to carbon cycling in marine sediments.
Chen, Haiwen; Holland, Paul
2010-01-01
In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…
Ising models and soliton equations
Perk, J.H.H.; Au-Yang, H.
1985-01-01
Several new results for the critical point of correlation functions of the Hirota equation are derived within the two-dimensional Ising model. The recent success of the conformal-invariance approach in the determination of a critical two-spin correration function is analyzed. The two-spin correlation function is predicted to be rotationally invariant and to decay with a power law in this approach. In the approach suggested here systematic corrections due to the underlying lattice breaking the rotational invariance are obtained
Linearized gyro-kinetic equation
Catto, P.J.; Tsang, K.T.
1976-01-01
An ordering of the linearized Fokker-Planck equation is performed in which gyroradius corrections are retained to lowest order and the radial dependence appropriate for sheared magnetic fields is treated without resorting to a WKB technique. This description is shown to be necessary to obtain the proper radial dependence when the product of the poloidal wavenumber and the gyroradius is large (k rho much greater than 1). A like particle collision operator valid for arbitrary k rho also has been derived. In addition, neoclassical, drift, finite β (plasma pressure/magnetic pressure), and unperturbed toroidal electric field modifications are treated
Generalized Ordinary Differential Equation Models.
Miao, Hongyu; Wu, Hulin; Xue, Hongqi
2014-10-01
Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data. The generalized ODE (GODE) model is therefore proposed and investigated for the first time. We develop the likelihood-based parameter estimation and inference methods for GODE models. We propose robust computing algorithms and rigorously investigate the asymptotic properties of the proposed estimator by considering both measurement errors and numerical errors in solving ODEs. The simulation study and application of our methods to an influenza viral dynamics study suggest that the proposed methods have a superior performance in terms of accuracy over the existing ODE model estimation approach and the extended smoothing-based (ESB) method.
BMN correlators by loop equations
Eynard, Bertrand; Kristjansen, Charlotte
2002-01-01
In the BMN approach to N=4 SYM a large class of correlators of interest are expressible in terms of expectation values of traces of words in a zero-dimensional gaussian complex matrix model. We develop a loop-equation based, analytic strategy for evaluating such expectation values to any order in the genus expansion. We reproduce the expectation values which were needed for the calculation of the one-loop, genus one correction to the anomalous dimension of BMN-operators and which were earlier obtained by combinatorial means. Furthermore, we present the expectation values needed for the calculation of the one-loop, genus two correction. (author)
Differential Equations and Computational Simulations
1999-06-18
given in (6),(7) in Taylor series of e. Equating coefficients of same power of e in both side of equity , we obtain a sequence of linear boundary value...fields, 3). structural instability and block stability of divergence-free vector fields on 2D compact manifolds with nonzero genus , and 4). structural...circle bands. Definition 3.1 Let N be a compact manifold without boundary and with genus k > 0. A closed domain fi C N is called a pseudo-manifold
Zhang, Yanxiang; Chen, Yu; Yan, Mufu
2017-07-01
The open circuit voltage (OCV) of solid oxide fuel cells is generally overestimated by the Nernst equation and the Wagner equation, due to the polarization losses at electrodes. Considering both the electronic conduction of electrolyte and the electrode polarization losses, we express the OCV as an implicit function of the characteristic oxygen pressure of electrolyte (p* [atm], at which the electronic and ionic conductivities are the same), and the relative polarization resistance of electrodes (rc = Rc/Ri and ra = Ra/Ri, where Ri/c/a [Ωcm2] denotes the ionic resistance of electrolyte, and the polarization resistances of cathode and anode, respectively). This equation approaches to the Wagner equation when the electrodes are highly active (rc and ra → 0), and approaches to the Nernst equation when the electrolyte is a purely ionic conductor (p* → 0). For the fuel cells whose OCV is well below the prediction of the Wagner equation, for example with thin doped ceria electrolyte, it is demonstrated that the combination of OCV and impedance spectroscopy measurements allows the determination of p*, Rc and Ra. This equation can serve as a simple yet powerful tool to study the internal losses in the cell under open circuit condition.
Introduction to partial differential equations with applications
Zachmanoglou, E C
1988-01-01
This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.
Integrable discretizations of the short pulse equation
Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro
2010-01-01
In this paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key construction is the bilinear form and determinant structure of solutions of the SP equation. We also give the determinant formulas of N-soliton solutions of the semi-discrete and full-discrete analogues of the SP equations, from which the multi-loop and multi-breather solutions can be generated. In the continuous limit, the full-discrete SP equation converges to the semi-discrete SP equation, and then to the continuous SP equation. Based on the semi-discrete SP equation, an integrable numerical scheme, i.e. a self-adaptive moving mesh scheme, is proposed and used for the numerical computation of the short pulse equation.
Random walk and the heat equation
Lawler, Gregory F
2010-01-01
The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation by considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equation and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. The first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For exa...
Oscillations of first order difference equations
Similarly, if yn < 0 for n ! N, then we may show that ... From Theorem 2 it follows that every solution of the equation oscillates. In particular, .... [2] Hartman P, Difference equations: Disconjugacy, principal solutions, Green's functions, complete ...
OSCILLATION OF NONLINEAR DELAY DIFFERENCE EQUATIONS
无
2006-01-01
This paper deals with the oscillatory properties of a class of nonlinear difference equations with several delays. Sufficient criteria in the form of infinite sum for the equations to be oscillatory are obtained.
OSCILLATION CRITERIA FOR FORCED SUPERLINEAR DIFFERENCE EQUATIONS
无
2008-01-01
Using Riccati transformation techniques,some oscillation criteria for the forced second-order superlinear difference equations are established.These criteria are dis- crete analogues of the criteria for differential equations proposed by Yan.
EXACT TRAVELLING WAVE SOLUTIONS TO BBM EQUATION
无
2009-01-01
Abundant new travelling wave solutions to the BBM (Benjamin-Bona-Mahoni) equation are obtained by the generalized Jacobian elliptic function method. This method can be applied to other nonlinear evolution equations.
Time-delay equation governing electron motion
Cohn, J.
1976-01-01
A previously proposed differential-difference equation governing the motion of the classical radiating electron is considered further. A set of three assumptions is offered, under which the proposed equation yields asymptotically stable acceleration
dimensional Nizhnik–Novikov–Veselov equations
2017-03-22
Mar 22, 2017 ... order differential equations with modified Riemann–Liouville derivatives into integer-order differential equations, ... tered in a variety of scientific and engineering fields ... devoted to the advanced calculus can be easily applied.
Linear superposition solutions to nonlinear wave equations
Liu Yu
2012-01-01
The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed
Extreme compression behaviour of equations of state
Shanker, J.; Dulari, P.; Singh, P.K.
2009-01-01
The extreme compression (P→∞) behaviour of various equations of state with K' ∞ >0 yields (P/K) ∞ =1/K' ∞ , an algebraic identity found by Stacey. Here P is the pressure, K the bulk modulus, K ' =dK/dP, and K' ∞ , the value of K ' at P→∞. We use this result to demonstrate further that there exists an algebraic identity also between the higher pressure derivatives of bulk modulus which is satisfied at extreme compression by different types of equations of state such as the Birch-Murnaghan equation, Poirier-Tarantola logarithmic equation, generalized Rydberg equation, Keane's equation and the Stacey reciprocal K-primed equation. The identity has been used to find a relationship between λ ∞ , the third-order Grueneisen parameter at P→∞, and pressure derivatives of bulk modulus with the help of the free-volume formulation without assuming any specific form of equation of state.
Metabolic profile of clinically severe obese patients.
Faria, Silvia Leite; Faria, Orlando Pereira; Menezes, Caroline Soares; de Gouvêa, Heloisa Rodrigues; de Almeida Cardeal, Mariane
2012-08-01
Since low basal metabolic rate (BMR) is a risk factor for weight regain, it is important to measure BMR before bariatric surgery. We aimed to evaluate the BMR among clinically severe obese patients preoperatively. We compared it with that of the control group, with predictive formulas and correlated it with body composition. We used indirect calorimetry (IC) to collect BMR data and multifrequency bioelectrical impedance to collect body composition data. Our sample population consisted of 193 patients of whom 130 were clinically severe obese and 63 were normal/overweight individuals. BMR results were compared with the following predictive formulas: Harris-Benedict (HBE), Bobbioni-Harsch (BH), Cunningham (CUN), Mifflin-St. Jeor (MSJE), and Horie-Waitzberg & Gonzalez (HW & G). This study was approved by the Ethics Committee for Research of the University of Brasilia. Statistical analysis was used to compare and correlate variables. Clinically severe obese patients had higher absolute BMR values and lower adjusted BMR values (p BMR were found in both groups. Among the clinically severe obese patients, the formulas of HW & G and HBE overestimated BMR values (p = 0.0002 and p = 0.0193, respectively), while the BH and CUN underestimated this value; only the MSJE formulas showed similar results to those of IC. The clinically severe obese patients showed low BMR levels when adjusted per kilogram per body weight. Body composition may influence BMR. The use of the MSJE formula may be helpful in those cases where it is impossible to use IC.
Partial differential equations of mathematical physics
Sobolev, S L
1964-01-01
Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems. The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method. Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied math
Baecklund transformations for integrable lattice equations
Atkinson, James
2008-01-01
We give new Baecklund transformations (BTs) for some known integrable (in the sense of being multidimensionally consistent) quadrilateral lattice equations. As opposed to the natural auto-BT inherent in every such equation, these BTs are of two other kinds. Specifically, it is found that some equations admit additional auto-BTs (with Baecklund parameter), whilst some pairs of apparently distinct equations admit a BT which connects them
New solutions of Heun's general equation
Ishkhanyan, Artur; Suominen, Kalle-Antti
2003-01-01
We show that in four particular cases the derivative of the solution of Heun's general equation can be expressed in terms of a solution to another Heun's equation. Starting from this property, we use the Gauss hypergeometric functions to construct series solutions to Heun's equation for the mentioned cases. Each of the hypergeometric functions involved has correct singular behaviour at only one of the singular points of the equation; the sum, however, has correct behaviour. (letter to the editor)
Notes on the infinity Laplace equation
Lindqvist, Peter
2016-01-01
This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures by the author. The Infinity.Laplace Equation has delightful counterparts to the Dirichlet integral, the mean value property, the Brownian motion, Harnack's inequality, and so on. This "fully non-linear" equation has applications to image processing and to mass transfer problems, and it provides optimal Lipschitz extensions of boundary values.
ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY
Enrique Gonzalo Reyes Garcia
2004-01-01
ON DIFFERENTIAL EQUATIONS, INTEGRABLE SYSTEMS, AND GEOMETRY Equations in partial derivatives appeared in the 18th century as essential tools for the analytic study of physical models and, later, they proved to be fundamental for the progress of mathematics. For example, fundamental results of modern differential geometry are based on deep theorems on differential equations. Reciprocally, it is possible to study differential equations through geometrical means just like it was done by o...
Hybrid quantum-classical master equations
Diósi, Lajos
2014-01-01
We discuss hybrid master equations of composite systems, which are hybrids of classical and quantum subsystems. A fairly general form of hybrid master equations is suggested. Its consistency is derived from the consistency of Lindblad quantum master equations. We emphasize that quantum measurement is a natural example of exact hybrid systems. We derive a heuristic hybrid master equation of time-continuous position measurement (monitoring). (paper)
On a complex differential Riccati equation
Khmelnytskaya, Kira V; Kravchenko, Vladislav V
2008-01-01
We consider a nonlinear partial differential equation for complex-valued functions which is related to the two-dimensional stationary Schroedinger equation and enjoys many properties similar to those of the ordinary differential Riccati equation such as the famous Euler theorems, the Picard theorem and others. Besides these generalizations of the classical 'one-dimensional' results, we discuss new features of the considered equation including an analogue of the Cauchy integral theorem
About the solvability of matrix polynomial equations
Netzer, Tim; Thom, Andreas
2016-01-01
We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd degree with non-degenerate leading form can be solved in self-adjoint matrices. We also study equations of even degree and equations in many variables.
On polynomial solutions of the Heun equation
Gurappa, N; Panigrahi, Prasanta K
2004-01-01
By making use of a recently developed method to solve linear differential equations of arbitrary order, we find a wide class of polynomial solutions to the Heun equation. We construct the series solution to the Heun equation before identifying the polynomial solutions. The Heun equation extended by the addition of a term, -σ/x, is also amenable for polynomial solutions. (letter to the editor)
New solutions of the confluent Heun equation
Harold Exton
1998-05-01
Full Text Available New compact triple series solutions of the confluent Heun equation (CHE are obtained by the appropriate applications of the Laplace transform and its inverse to a suitably constructed system of soluble differential equations. The computer-algebra package MAPLE V is used to tackle an auxiliary system of non-linear algebraic equations. This study is partly motivated by the relationship between the CHE and certain Schrödininger equations.
Some Aspects of Extended Kinetic Equation
Dilip Kumar
2015-09-01
Full Text Available Motivated by the pathway model of Mathai introduced in 2005 [Linear Algebra and Its Applications, 396, 317–328] we extend the standard kinetic equations. Connection of the extended kinetic equation with fractional calculus operator is established. The solution of the general form of the fractional kinetic equation is obtained through Laplace transform. The results for the standard kinetic equation are obtained as the limiting case.
Solutions manual to accompany Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
PARALLEL SOLUTION METHODS OF PARTIAL DIFFERENTIAL EQUATIONS
Korhan KARABULUT
1998-03-01
Full Text Available Partial differential equations arise in almost all fields of science and engineering. Computer time spent in solving partial differential equations is much more than that of in any other problem class. For this reason, partial differential equations are suitable to be solved on parallel computers that offer great computation power. In this study, parallel solution to partial differential equations with Jacobi, Gauss-Siedel, SOR (Succesive OverRelaxation and SSOR (Symmetric SOR algorithms is studied.
Non-markovian boltzmann equation
Kremp, D.; Bonitz, M.; Kraeft, W.D.; Schlanges, M.
1997-01-01
A quantum kinetic equation for strongly interacting particles (generalized binary collision approximation, ladder or T-matrix approximation) is derived in the framework of the density operator technique. In contrast to conventional kinetic theory, which is valid on large time scales as compared to the collision (correlation) time only, our approach retains the full time dependencies, especially also on short time scales. This means retardation and memory effects resulting from the dynamics of binary correlations and initial correlations are included. Furthermore, the resulting kinetic equation conserves total energy (the sum of kinetic and potential energy). The second aspect of generalization is the inclusion of many-body effects, such as self-energy, i.e., renormalization of single-particle energies and damping. To this end we introduce an improved closure relation to the Bogolyubov endash Born endash Green endash Kirkwood endash Yvon hierarchy. Furthermore, in order to express the collision integrals in terms of familiar scattering quantities (Mo/ller operator, T-matrix), we generalize the methods of quantum scattering theory by the inclusion of medium effects. To illustrate the effects of memory and damping, the results of numerical simulations are presented. copyright 1997 Academic Press, Inc
Dutta, Gaurav
2016-10-12
Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. The amplitude and the dispersion losses from attenuation are often compensated for during prestack depth migration. However, most attenuation compensation or Qcompensation migration algorithms require an estimate of the background Q model. We have developed a wave-equation gradient optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ∈, where ∈ is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early arrivals. The gradient is computed by migrating the observed traces weighted by the frequency shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests determined that an improved accuracy of the Q model by wave-equation Q tomography leads to a noticeable improvement in migration image quality. © 2016 Society of Exploration Geophysicists.
Quantization of Equations of Motion
D. Kochan
2007-01-01
Full Text Available The Classical Newton-Lagrange equations of motion represent the fundamental physical law of mechanics. Their traditional Lagrangian and/or Hamiltonian precursors when available are essential in the context of quantization. However, there are situations that lack Lagrangian and/or Hamiltonian settings. This paper discusses a description of classical dynamics and presents some irresponsible speculations about its quantization by introducing a certain canonical two-form ?. By its construction ? embodies kinetic energy and forces acting within the system (not their potential. A new type of variational principle employing differential two-form ? is introduced. Variation is performed over “umbilical surfaces“ instead of system histories. It provides correct Newton-Lagrange equations of motion. The quantization is inspired by the Feynman path integral approach. The quintessence is to rearrange it into an “umbilical world-sheet“ functional integral in accordance with the proposed variational principle. In the case of potential-generated forces, the new approach reduces to the standard quantum mechanics. As an example, Quantum Mechanics with friction is analyzed in detail.
Sobolev gradients and differential equations
Neuberger, J W
2010-01-01
A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair p...
Dutta, Gaurav; Schuster, Gerard T.
2016-01-01
Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. The amplitude and the dispersion losses from attenuation are often compensated for during prestack depth migration. However, most attenuation compensation or Qcompensation migration algorithms require an estimate of the background Q model. We have developed a wave-equation gradient optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ∈, where ∈ is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early arrivals. The gradient is computed by migrating the observed traces weighted by the frequency shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests determined that an improved accuracy of the Q model by wave-equation Q tomography leads to a noticeable improvement in migration image quality. © 2016 Society of Exploration Geophysicists.
The Laplace transformation of adjoint transport equations
Hoogenboom, J.E.
1985-01-01
A clarification is given of the difference between the equation adjoint to the Laplace-transformed time-dependent transport equation and the Laplace-transformed time-dependent adjoint transport equation. Proper procedures are derived to obtain the Laplace transform of the instantaneous detector response. (author)
Equations of state for light water
Rubin, G.A.; Granziera, M.R.
1983-01-01
The equations of state for light water were developed, based on the tables of Keenan and Keyes. Equations are presented, describing the specific volume, internal energy, enthalpy and entropy of saturated steam, superheated vapor and subcooled liquid as a function of pressure and temperature. For each property, several equations are shown, with different precisions and different degress of complexity. (Author) [pt
Cole's ansatz and extensions of Burgers' equation
Tasso, H.
1976-01-01
A sequence of nonlinear partial differential equations is constructed. It contains all equation whose solutions can be obtained from applying the Cole-Hopf transformation to linear partial differential equations. An exemple is usub(t) = (u 3 )sub(x) + 3/2(u 2 )sub(xx) + usub(xxx). (orig.) [de
Completely integrable operator evolution equations. II
Chudnovsky, D.V.
1979-01-01
The author continues the investigation of operator classical completely integrable systems. The main attention is devoted to the stationary operator non-linear Schroedinger equation. It is shown that this equation can be used for separation of variables for a large class of completely integrable equations. (Auth.)
Derivation of the neutron diffusion equation
Mika, J.R.; Banasiak, J.
1994-01-01
We discuss the diffusion equation as an asymptotic limit of the neutron transport equation for large scattering cross sections. We show that the classical asymptotic expansion procedure does not lead to the diffusion equation and present two modified approaches to overcome this difficulty. The effect of the initial layer is also discussed. (authors). 9 refs
Skew differential fields, differential and difference equations
van der Put, M
2004-01-01
The central question is: Let a differential or difference equation over a field K be isomorphic to all its Galois twists w.r.t. the group Gal(K/k). Does the equation descend to k? For a number of categories of equations an answer is given.
Some Functional Equations Originating from Number Theory
We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.
A reliable treatment for nonlinear Schroedinger equations
Khani, F.; Hamedi-Nezhad, S.; Molabahrami, A.
2007-01-01
Exp-function method is used to find a unified solution of nonlinear wave equation. Nonlinear Schroedinger equations with cubic and power law nonlinearity are selected to illustrate the effectiveness and simplicity of the method. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear equation
New solitons connected to the Dirac equation
Grosse, H.
1984-01-01
Imposing isospectral invariance for the one dimensional Dirac operator leads to systems of nonlinear partial differential equations. By constructing reflectionless potentials of the Dirac equation we obtain a new type of solitons for a system of modified Korteweg-de Vries equations. (Author)
Compositeness condition in the renormalization group equation
Bando, Masako; Kugo, Taichiro; Maekawa, Nobuhiro; Sasakura, Naoki; Watabiki, Yoshiyuki; Suehiro, Kazuhiko
1990-01-01
The problems in imposing compositeness conditions as boundary conditions in renormalization group equations are discussed. It is pointed out that one has to use the renormalization group equation directly in cutoff theory. In some cases, however, it can be approximated by the renormalization group equation in continuum theory if the mass dependent renormalization scheme is adopted. (orig.)
Transformation properties of the integrable evolution equations
Konopelchenko, B.G.
1981-01-01
Group-theoretical properties of partial differential equations integrable by the inverse scattering transform method are discussed. It is shown that nonlinear transformations typical to integrable equations (symmetry groups, Baecklund-transformations) and these equations themselves are contained in a certain universal nonlinear transformation group. (orig.)
Comparison of the Schrodinger and Salpeter equations
Jacobs, S.; Olsson, M.G.
1985-01-01
A unified approach to the solution of the Schrodinger and spinless Salpeter equations is presented. Fits to heavy quark bound state energies using various potential models are employed to determine whether the Salpeter equation provides a better description of heavy quark systems than the Schrodinger equation
Lie symmetries for systems of evolution equations
Paliathanasis, Andronikos; Tsamparlis, Michael
2018-01-01
The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the differential equations. The exact relation of the Lie symmetries with the collineations of the bimetric space is determined.
Loop equations in the theory of gravitation
Makeenko, Yu.M.; Voronov, N.A.
1981-01-01
Loop-space variables (matrices of parallel transport) for the theory of gravitation are described. Loop equations, which are equivalent to the Einstein equations, are derived in the classical case. Loop equations are derived for gravity with cosmological constant as well. An analogy with the loop-space approach in Yang-Mills theory is discussed [ru
Symmetry properties of fractional diffusion equations
Gazizov, R K; Kasatkin, A A; Lukashchuk, S Yu [Ufa State Aviation Technical University, Karl Marx strausse 12, Ufa (Russian Federation)], E-mail: gazizov@mail.rb.ru, E-mail: alexei_kasatkin@mail.ru, E-mail: lsu@mail.rb.ru
2009-10-15
In this paper, nonlinear anomalous diffusion equations with time fractional derivatives (Riemann-Liouville and Caputo) of the order of 0-2 are considered. Lie point symmetries of these equations are investigated and compared. Examples of using the obtained symmetries for constructing exact solutions of the equations under consideration are presented.
More Issues in Observed-Score Equating
van der Linden, Wim J.
2013-01-01
This article is a response to the commentaries on the position paper on observed-score equating by van der Linden (this issue). The response focuses on the more general issues in these commentaries, such as the nature of the observed scores that are equated, the importance of test-theory assumptions in equating, the necessity to use multiple…
Solving Absolute Value Equations Algebraically and Geometrically
Shiyuan, Wei
2005-01-01
The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.
Antishadowing effects in the unitarized BFKL equation
Ruan Jianhong; Shen Zhenqi; Yang Jifeng; Zhu Wei
2007-01-01
A unitarized BFKL equation incorporating shadowing and antishadowing corrections of the gluon recombination is proposed. This equation reduces to the Balitsky-Kovchegov evolution equation near the saturation limit. We find that the antishadowing effects have a sizable influence on the gluon distribution function in the preasymptotic regime
Antishadowing effects in the unitarized BFKL equation
Ruan Jianhong [Department of Physics, East China Normal University, Shanghai 200062 (China); Shen Zhenqi [Department of Physics, East China Normal University, Shanghai 200062 (China); Yang Jifeng [Department of Physics, East China Normal University, Shanghai 200062 (China); Zhu Wei [Department of Physics, East China Normal University, Shanghai 200062 (China)]. E-mail: weizhu@mail.ecnu.edu.cn
2007-01-01
A unitarized BFKL equation incorporating shadowing and antishadowing corrections of the gluon recombination is proposed. This equation reduces to the Balitsky-Kovchegov evolution equation near the saturation limit. We find that the antishadowing effects have a sizable influence on the gluon distribution function in the preasymptotic regime.
Local Observed-Score Kernel Equating
Wiberg, Marie; van der Linden, Wim J.; von Davier, Alina A.
2014-01-01
Three local observed-score kernel equating methods that integrate methods from the local equating and kernel equating frameworks are proposed. The new methods were compared with their earlier counterparts with respect to such measures as bias--as defined by Lord's criterion of equity--and percent relative error. The local kernel item response…
The Modified Enskog Equation for Mixtures
Beijeren, H. van; Ernst, M.H.
1973-01-01
In a previous paper it was shown that a modified form of the Enskog equation, applied to mixtures of hard spheres, should be considered as the correct extension of the usual Enskog equation to the case of mixtures. The main argument was that the modified Enskog equation leads to linear transport
Jacobi equations as Lagrange equations of the deformed Lagrangian
Casciaro, B.
1995-03-01
We study higher-order variational derivatives of a generic Lagrangian L 0 = L 0 (t,q,q). We introduce two new Lagrangians, L 1 and L 2 , associated to the first and second-order deformations of the original Lagrangian L 0 . In terms of these Lagrangians, we are able to establish simple relations between the variational derivatives of different orders of a Lagrangian. As a consequence of these relations the Euler-Lagrange and the Jacobi equations are obtained from a single variational principle based on L 1 . We can furthermore introduce an associated Hamiltonian H 1 = H 1 (t,q,q radical,η,η radical) with η equivalent to δq. If L 0 is independent of time then H 1 is a conserved quantity. (author). 15 refs
The Dirac equation and its solutions
Bagrov, Vladislav G. [Tomsk State Univ., Tomsk (Russian Federation). Dept. of Quantum Field Theroy; Gitman, Dmitry [Sao Paulo Univ. (Brazil). Inst. de Fisica; P.N. Lebedev Physical Institute, Moscow (Russian Federation); Tomsk State Univ., Tomsk (Russian Federation). Faculty of Physics
2013-07-01
The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.
The Dirac equation and its solutions
Bagrov, Vladislav G
2014-01-01
Dirac equations are of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly.In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.
An integral transform of the Salpeter equation
Krolikowski, W.
1980-03-01
We find a new form of relativistic wave equation for two spin-1/2 particles, which arises by an integral transformation (in the position space) of the wave function in the Salpeter equation. The non-locality involved in this transformation is extended practically over the Compton wavelength of the lighter of two particles. In the case of equal masses the new equation assumes the form of the Breit equation with an effective integral interaction. In the one-body limit it reduces to the Dirac equation also with an effective integral interaction. (author)
Sparse dynamics for partial differential equations.
Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D; Osher, Stanley
2013-04-23
We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms.
Numerical methods for differential equations and applications
Ixaru, L.G.
1984-01-01
This book is addressed to persons who, without being professionals in applied mathematics, are often faced with the problem of numerically solving differential equations. In each of the first three chapters a definite class of methods is discussed for the solution of the initial value problem for ordinary differential equations: multistep methods; one-step methods; and piecewise perturbation methods. The fourth chapter is mainly focussed on the boundary value problems for linear second-order equations, with a section devoted to the Schroedinger equation. In the fifth chapter the eigenvalue problem for the radial Schroedinger equation is solved in several ways, with computer programs included. (Auth.)
The Dirac equation and its solutions
Bagrov, Vladislav G.; Gitman, Dmitry; P.N. Lebedev Physical Institute, Moscow; Tomsk State Univ., Tomsk
2013-01-01
The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.